1.2. A Quantum System. Consider the system with hamiltonian H = H0...

Question
Solution Preview

These solutions may offer step-by-step problem-solving explanations or good writing examples that include modern styles of formatting and construction of bibliographies out of text citations and references.
Students may use these solutions for personal skill-building and practice.
Unethical use is strictly forbidden.

This is only a preview of the solution.
Please use the purchase button to see the entire solution.
By purchasing this solution you'll be able to access the following files:
Solution.pdf
Purchase Solution
$55.00
Google Pay
Amazon
Paypal
Mastercard
Visacard
Discover
Amex
View Available Physics Tutors 529 tutors matched
ionut
Ionut
(ionut)
Hi! MSc Applied Informatics & Computer Science Engineer. Practical experience in many CS & IT branches.Research work & homework
5/5 (5,654+ sessions)
2 hours avg response
Leo
Leo
(Leo)
Hi! I have been a professor in New York and taught in a math department and in an applied math department.
4.9/5 (5,652+ sessions)
2 hours avg response
Pranay
(math1983)
Ph.D. in mathematics and working as an Assistant Professor in University. I can provide help in mathematics, statistics and allied areas.
4.6/5 (5,512+ sessions)
1 hour avg response

Similar Homework Solutions

8.1.0PHP Version674msRequest Duration45MBMemory UsageGET college-homework-library/{category}/{subject}/{id}Route
    • Booting (348ms)time
    • Application (326ms)time
    • 1 x Booting (51.63%)
      348ms
      1 x Application (48.37%)
      326ms
      • Illuminate\Routing\Events\Routing (1.42ms)
      • Illuminate\Routing\Events\RouteMatched (523μs)
      • Illuminate\Foundation\Events\LocaleUpdated (4.7ms)
      • eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibrary (229μs)
      • eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibrary (206μs)
      • Illuminate\Database\Events\ConnectionEstablished (1.5ms)
      • Illuminate\Database\Events\StatementPrepared (22.79ms)
      • Illuminate\Database\Events\QueryExecuted (1.41ms)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (142μs)
      • eloquent.booting: App\Models\Subject (137μs)
      • eloquent.booted: App\Models\Subject (61μs)
      • Illuminate\Database\Events\StatementPrepared (5.42ms)
      • Illuminate\Database\Events\QueryExecuted (2.91ms)
      • eloquent.retrieved: App\Models\Subject (160μs)
      • eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibraryFile (247μs)
      • eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibraryFile (65μs)
      • Illuminate\Database\Events\StatementPrepared (834μs)
      • Illuminate\Database\Events\QueryExecuted (1.85ms)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (113μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (16μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (9μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (6μs)
      • eloquent.booting: App\Models\SubjectCat (278μs)
      • eloquent.booted: App\Models\SubjectCat (42μs)
      • Illuminate\Database\Events\StatementPrepared (2.67ms)
      • Illuminate\Database\Events\QueryExecuted (3.26ms)
      • eloquent.retrieved: App\Models\SubjectCat (106μs)
      • Illuminate\Cache\Events\CacheHit (18.68ms)
      • Illuminate\Cache\Events\CacheMissed (954μs)
      • Illuminate\Database\Events\StatementPrepared (1.22ms)
      • Illuminate\Database\Events\QueryExecuted (15.51ms)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (490μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (52μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (17μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (15μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (12μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (12μs)
      • Illuminate\Database\Events\StatementPrepared (778μs)
      • Illuminate\Database\Events\QueryExecuted (1.49ms)
      • eloquent.retrieved: App\Models\Subject (151μs)
      • Illuminate\Cache\Events\KeyWritten (1.61ms)
      • Illuminate\Database\Events\StatementPrepared (2.59ms)
      • Illuminate\Database\Events\QueryExecuted (2.04ms)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (53μs)
      • Illuminate\Database\Events\StatementPrepared (1.23ms)
      • Illuminate\Database\Events\QueryExecuted (1.52ms)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (84μs)
      • Illuminate\Database\Events\StatementPrepared (1.07ms)
      • Illuminate\Database\Events\QueryExecuted (1.73ms)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (40μs)
      • Illuminate\Cache\Events\CacheHit (815μs)
      • creating: homework.show (1.19ms)
      • composing: homework.show (291μs)
      • creating: components.breadcrumbs (402μs)
      • composing: components.breadcrumbs (624μs)
      • Illuminate\Database\Events\StatementPrepared (1.49ms)
      • Illuminate\Database\Events\QueryExecuted (1.06ms)
      • eloquent.retrieved: App\Models\SubjectCat (98μs)
      • Illuminate\Cache\Events\CacheMissed (9.31ms)
      • Illuminate\Database\Events\StatementPrepared (866μs)
      • Illuminate\Database\Events\QueryExecuted (2.06ms)
      • eloquent.retrieved: App\Models\SubjectCat (248μs)
      • Illuminate\Cache\Events\KeyWritten (625μs)
      • Illuminate\Cache\Events\CacheHit (704μs)
      • Illuminate\Cache\Events\CacheHit (387μs)
      • Illuminate\Cache\Events\CacheHit (218μs)
      • Illuminate\Cache\Events\CacheHit (187μs)
      • Illuminate\Cache\Events\CacheHit (164μs)
      • Illuminate\Cache\Events\CacheHit (183μs)
      • Illuminate\Cache\Events\CacheHit (161μs)
      • Illuminate\Cache\Events\CacheHit (514μs)
      • Illuminate\Cache\Events\CacheHit (179μs)
      • Illuminate\Cache\Events\CacheHit (185μs)
      • Illuminate\Cache\Events\CacheHit (480μs)
      • Illuminate\Cache\Events\CacheHit (213μs)
      • Illuminate\Cache\Events\CacheHit (234μs)
      • Illuminate\Cache\Events\CacheMissed (199μs)
      • Illuminate\Database\Events\StatementPrepared (988μs)
      • Illuminate\Database\Events\QueryExecuted (1.5ms)
      • eloquent.retrieved: App\Models\SubjectCat (78μs)
      • Illuminate\Cache\Events\KeyWritten (952μs)
      • Illuminate\Cache\Events\CacheHit (630μs)
      • Illuminate\Cache\Events\CacheHit (382μs)
      • Illuminate\Cache\Events\CacheHit (552μs)
      • Illuminate\Cache\Events\CacheHit (282μs)
      • Illuminate\Cache\Events\CacheHit (219μs)
      • Illuminate\Cache\Events\CacheHit (621μs)
      • Illuminate\Cache\Events\CacheHit (417μs)
      • Illuminate\Cache\Events\CacheMissed (7.2ms)
      • Illuminate\Database\Events\StatementPrepared (4.45ms)
      • Illuminate\Database\Events\QueryExecuted (3.66ms)
      • eloquent.retrieved: App\Models\SubjectCat (95μs)
      • Illuminate\Cache\Events\KeyWritten (6.89ms)
      • Illuminate\Cache\Events\CacheHit (1.94ms)
      • Illuminate\Cache\Events\CacheHit (790μs)
      • Illuminate\Cache\Events\CacheHit (5.17ms)
      • Illuminate\Cache\Events\CacheHit (1.29ms)
      • Illuminate\Cache\Events\CacheHit (503μs)
      • Illuminate\Cache\Events\CacheHit (607μs)
      • Illuminate\Cache\Events\CacheHit (589μs)
      • Illuminate\Cache\Events\CacheHit (1.92ms)
      • Illuminate\Cache\Events\CacheHit (2.09ms)
      • Illuminate\Cache\Events\CacheHit (1.11ms)
      • Illuminate\Cache\Events\CacheHit (1.37ms)
      • Illuminate\Cache\Events\CacheHit (1.29ms)
      • Illuminate\Cache\Events\CacheHit (215μs)
      • Illuminate\Cache\Events\CacheHit (231μs)
      • Illuminate\Cache\Events\CacheHit (190μs)
      • Illuminate\Cache\Events\CacheHit (201μs)
      • Illuminate\Cache\Events\CacheHit (170μs)
      • Illuminate\Cache\Events\CacheHit (192μs)
      • Illuminate\Cache\Events\CacheHit (168μs)
      • Illuminate\Cache\Events\CacheHit (192μs)
      • Illuminate\Cache\Events\CacheHit (167μs)
      • Illuminate\Cache\Events\CacheHit (206μs)
      • Illuminate\Cache\Events\CacheHit (171μs)
      • Illuminate\Cache\Events\CacheHit (205μs)
      • Illuminate\Cache\Events\CacheHit (1.41ms)
      • Illuminate\Cache\Events\CacheHit (252μs)
      • Illuminate\Cache\Events\CacheHit (200μs)
      • Illuminate\Cache\Events\CacheHit (223μs)
      • Illuminate\Cache\Events\CacheHit (195μs)
      • Illuminate\Cache\Events\CacheHit (216μs)
      • Illuminate\Cache\Events\CacheHit (588μs)
      • Illuminate\Cache\Events\CacheMissed (333μs)
      • Illuminate\Database\Events\StatementPrepared (839μs)
      • Illuminate\Database\Events\QueryExecuted (1.35ms)
      • eloquent.retrieved: App\Models\SubjectCat (62μs)
      • Illuminate\Cache\Events\KeyWritten (426μs)
      • Illuminate\Cache\Events\CacheHit (1.34ms)
      • Illuminate\Cache\Events\CacheHit (318μs)
      • Illuminate\Cache\Events\CacheHit (186μs)
      • Illuminate\Cache\Events\CacheHit (234μs)
      • Illuminate\Cache\Events\CacheHit (265μs)
      • Illuminate\Cache\Events\CacheHit (390μs)
      • Illuminate\Cache\Events\CacheHit (181μs)
      • Illuminate\Cache\Events\CacheHit (346μs)
      • Illuminate\Cache\Events\CacheHit (199μs)
      • Illuminate\Cache\Events\CacheHit (193μs)
      • Illuminate\Cache\Events\CacheHit (190μs)
      • Illuminate\Cache\Events\CacheHit (808μs)
      • Illuminate\Cache\Events\CacheHit (268μs)
      • Illuminate\Cache\Events\CacheHit (423μs)
      • Illuminate\Cache\Events\CacheHit (314μs)
      • Illuminate\Cache\Events\CacheHit (249μs)
      • Illuminate\Cache\Events\CacheHit (997μs)
      • Illuminate\Cache\Events\CacheHit (355μs)
      • Illuminate\Cache\Events\CacheHit (258μs)
      • Illuminate\Cache\Events\CacheHit (208μs)
      • Illuminate\Cache\Events\CacheHit (198μs)
      • Illuminate\Cache\Events\CacheHit (200μs)
      • Illuminate\Cache\Events\CacheHit (193μs)
      • Illuminate\Cache\Events\CacheHit (888μs)
      • Illuminate\Cache\Events\CacheHit (221μs)
      • Illuminate\Cache\Events\CacheHit (200μs)
      • Illuminate\Cache\Events\CacheHit (588μs)
      • Illuminate\Cache\Events\CacheHit (444μs)
      • Illuminate\Cache\Events\CacheHit (544μs)
      • Illuminate\Cache\Events\CacheHit (364μs)
      • Illuminate\Cache\Events\CacheHit (257μs)
      • Illuminate\Cache\Events\CacheHit (349μs)
      • Illuminate\Cache\Events\CacheHit (294μs)
      • Illuminate\Cache\Events\CacheHit (302μs)
      • Illuminate\Cache\Events\CacheHit (192μs)
      • Illuminate\Cache\Events\CacheHit (199μs)
      • Illuminate\Cache\Events\CacheHit (170μs)
      • Illuminate\Cache\Events\CacheHit (199μs)
      • Illuminate\Cache\Events\CacheHit (182μs)
      • Illuminate\Cache\Events\CacheMissed (521μs)
      • Illuminate\Database\Events\StatementPrepared (824μs)
      • Illuminate\Database\Events\QueryExecuted (2.1ms)
      • eloquent.retrieved: App\Models\SubjectCat (161μs)
      • Illuminate\Cache\Events\KeyWritten (415μs)
      • Illuminate\Cache\Events\CacheHit (1.19ms)
      • Illuminate\Cache\Events\CacheHit (413μs)
      • Illuminate\Cache\Events\CacheHit (251μs)
      • Illuminate\Cache\Events\CacheHit (191μs)
      • Illuminate\Cache\Events\CacheHit (194μs)
      • Illuminate\Cache\Events\CacheHit (419μs)
      • Illuminate\Cache\Events\CacheHit (261μs)
      • Illuminate\Cache\Events\CacheMissed (386μs)
      • Illuminate\Database\Events\StatementPrepared (863μs)
      • Illuminate\Database\Events\QueryExecuted (1.16ms)
      • eloquent.retrieved: App\Models\SubjectCat (207μs)
      • Illuminate\Cache\Events\KeyWritten (3.52ms)
      • Illuminate\Cache\Events\CacheHit (3.22ms)
      • Illuminate\Cache\Events\CacheHit (348μs)
      • Illuminate\Cache\Events\CacheHit (298μs)
      • Illuminate\Cache\Events\CacheHit (415μs)
      • Illuminate\Cache\Events\CacheHit (209μs)
      • Illuminate\Cache\Events\CacheHit (349μs)
      • Illuminate\Cache\Events\CacheHit (200μs)
      • Illuminate\Cache\Events\CacheHit (254μs)
      • Illuminate\Cache\Events\CacheHit (165μs)
      • Illuminate\Cache\Events\CacheHit (1.4ms)
      • Illuminate\Cache\Events\CacheHit (224μs)
      • Illuminate\Cache\Events\CacheHit (2.4ms)
      • Illuminate\Cache\Events\CacheHit (282μs)
      • Illuminate\Cache\Events\CacheHit (259μs)
      • Illuminate\Cache\Events\CacheHit (228μs)
      • Illuminate\Cache\Events\CacheHit (364μs)
      • Illuminate\Cache\Events\CacheHit (168μs)
      • Illuminate\Cache\Events\CacheHit (286μs)
      • Illuminate\Cache\Events\CacheHit (239μs)
      • Illuminate\Cache\Events\CacheHit (395μs)
      • Illuminate\Cache\Events\CacheHit (177μs)
      • Illuminate\Cache\Events\CacheHit (184μs)
      • Illuminate\Cache\Events\CacheHit (162μs)
      • Illuminate\Cache\Events\CacheHit (194μs)
      • Illuminate\Cache\Events\CacheHit (833μs)
      • Illuminate\Cache\Events\CacheHit (194μs)
      • Illuminate\Cache\Events\CacheHit (365μs)
      • Illuminate\Cache\Events\CacheHit (331μs)
      • Illuminate\Cache\Events\CacheHit (196μs)
      • Illuminate\Cache\Events\CacheMissed (192μs)
      • Illuminate\Database\Events\StatementPrepared (759μs)
      • Illuminate\Database\Events\QueryExecuted (968μs)
      • eloquent.retrieved: App\Models\SubjectCat (100μs)
      • Illuminate\Cache\Events\KeyWritten (1.62ms)
      • Illuminate\Cache\Events\CacheHit (239μs)
      • Illuminate\Cache\Events\CacheHit (320μs)
      • Illuminate\Cache\Events\CacheHit (229μs)
      • Illuminate\Cache\Events\CacheHit (464μs)
      • Illuminate\Cache\Events\CacheHit (527μs)
      • Illuminate\Cache\Events\CacheHit (671μs)
      • Illuminate\Cache\Events\CacheHit (391μs)
      • Illuminate\Cache\Events\CacheHit (210μs)
      • Illuminate\Cache\Events\CacheHit (244μs)
      • Illuminate\Cache\Events\CacheHit (186μs)
      • Illuminate\Cache\Events\CacheHit (251μs)
      • Illuminate\Cache\Events\CacheHit (338μs)
      • Illuminate\Cache\Events\CacheHit (277μs)
      • Illuminate\Cache\Events\CacheHit (188μs)
      • Illuminate\Cache\Events\CacheHit (167μs)
      • Illuminate\Cache\Events\CacheHit (183μs)
      • Illuminate\Cache\Events\CacheHit (222μs)
      • Illuminate\Cache\Events\CacheHit (218μs)
      • Illuminate\Cache\Events\CacheHit (176μs)
      • Illuminate\Cache\Events\CacheHit (189μs)
      • Illuminate\Cache\Events\CacheHit (167μs)
      • Illuminate\Cache\Events\CacheHit (178μs)
      • Illuminate\Cache\Events\CacheHit (779μs)
      • Illuminate\Cache\Events\CacheHit (726μs)
      • Illuminate\Cache\Events\CacheHit (1.31ms)
      • Illuminate\Cache\Events\CacheHit (210μs)
      • Illuminate\Cache\Events\CacheHit (747μs)
      • Illuminate\Cache\Events\CacheHit (197μs)
      • Illuminate\Cache\Events\CacheHit (1.39ms)
      • Illuminate\Cache\Events\CacheHit (517μs)
      • Illuminate\Cache\Events\CacheHit (297μs)
      • Illuminate\Cache\Events\CacheHit (233μs)
      • Illuminate\Cache\Events\CacheHit (332μs)
      • Illuminate\Cache\Events\CacheHit (207μs)
      • Illuminate\Cache\Events\CacheHit (164μs)
      • Illuminate\Cache\Events\CacheHit (692μs)
      • Illuminate\Cache\Events\CacheHit (973μs)
      • Illuminate\Cache\Events\CacheHit (817μs)
      • Illuminate\Cache\Events\CacheHit (1.18ms)
      • Illuminate\Cache\Events\CacheHit (690μs)
      • Illuminate\Cache\Events\CacheHit (501μs)
      • Illuminate\Cache\Events\CacheHit (953μs)
      • Illuminate\Cache\Events\CacheHit (450μs)
      • Illuminate\Cache\Events\CacheHit (1.57ms)
      • Illuminate\Cache\Events\CacheHit (1.95ms)
      • Illuminate\Cache\Events\CacheHit (320μs)
      • Illuminate\Cache\Events\CacheHit (263μs)
      • Illuminate\Cache\Events\CacheHit (1.57ms)
      • Illuminate\Cache\Events\CacheHit (630μs)
      • Illuminate\Cache\Events\CacheHit (335μs)
      • Illuminate\Cache\Events\CacheHit (443μs)
      • Illuminate\Cache\Events\CacheHit (567μs)
      • Illuminate\Cache\Events\CacheHit (194μs)
      • Illuminate\Cache\Events\CacheHit (705μs)
      • Illuminate\Cache\Events\CacheHit (718μs)
      • Illuminate\Cache\Events\CacheHit (414μs)
      • Illuminate\Cache\Events\CacheHit (272μs)
      • Illuminate\Cache\Events\CacheHit (192μs)
      • Illuminate\Cache\Events\CacheHit (166μs)
      • Illuminate\Cache\Events\CacheHit (305μs)
      • Illuminate\Cache\Events\CacheHit (273μs)
      • Illuminate\Cache\Events\CacheHit (203μs)
      • Illuminate\Cache\Events\CacheHit (217μs)
      • Illuminate\Cache\Events\CacheMissed (202μs)
      • Illuminate\Database\Events\StatementPrepared (1.76ms)
      • Illuminate\Database\Events\QueryExecuted (1.37ms)
      • eloquent.retrieved: App\Models\SubjectCat (108μs)
      • Illuminate\Cache\Events\KeyWritten (438μs)
      • Illuminate\Cache\Events\CacheHit (1.58ms)
      • Illuminate\Cache\Events\CacheHit (312μs)
      • Illuminate\Cache\Events\CacheHit (280μs)
      • Illuminate\Cache\Events\CacheHit (279μs)
      • Illuminate\Cache\Events\CacheHit (383μs)
      • Illuminate\Cache\Events\CacheHit (666μs)
      • Illuminate\Cache\Events\CacheHit (665μs)
      • Illuminate\Cache\Events\CacheHit (222μs)
      • Illuminate\Cache\Events\CacheHit (801μs)
      • Illuminate\Cache\Events\CacheHit (253μs)
      • Illuminate\Cache\Events\CacheHit (380μs)
      • Illuminate\Cache\Events\CacheHit (204μs)
      • Illuminate\Cache\Events\CacheHit (226μs)
      • Illuminate\Cache\Events\CacheHit (350μs)
      • Illuminate\Cache\Events\CacheHit (228μs)
      • Illuminate\Cache\Events\CacheHit (228μs)
      • Illuminate\Cache\Events\CacheHit (233μs)
      • Illuminate\Cache\Events\CacheHit (1.47ms)
      • Illuminate\Cache\Events\CacheHit (409μs)
      • Illuminate\Cache\Events\CacheHit (336μs)
      • Illuminate\Cache\Events\CacheHit (180μs)
      • Illuminate\Cache\Events\CacheHit (183μs)
      • Illuminate\Cache\Events\CacheHit (159μs)
      • Illuminate\Cache\Events\CacheHit (180μs)
      • Illuminate\Cache\Events\CacheHit (160μs)
      • Illuminate\Cache\Events\CacheHit (246μs)
      • Illuminate\Cache\Events\CacheHit (211μs)
      • Illuminate\Cache\Events\CacheHit (187μs)
      • Illuminate\Cache\Events\CacheHit (163μs)
      • Illuminate\Cache\Events\CacheHit (179μs)
      • Illuminate\Cache\Events\CacheHit (330μs)
      • Illuminate\Cache\Events\CacheHit (197μs)
      • Illuminate\Cache\Events\CacheHit (163μs)
      • Illuminate\Cache\Events\CacheHit (263μs)
      • Illuminate\Cache\Events\CacheHit (164μs)
      • Illuminate\Cache\Events\CacheHit (272μs)
      • Illuminate\Cache\Events\CacheHit (206μs)
      • Illuminate\Cache\Events\CacheHit (314μs)
      • Illuminate\Cache\Events\CacheHit (180μs)
      • Illuminate\Cache\Events\CacheHit (191μs)
      • Illuminate\Cache\Events\CacheHit (229μs)
      • Illuminate\Cache\Events\CacheHit (188μs)
      • Illuminate\Cache\Events\CacheHit (161μs)
      • Illuminate\Cache\Events\CacheHit (179μs)
      • Illuminate\Cache\Events\CacheHit (166μs)
      • Illuminate\Cache\Events\CacheHit (236μs)
      • Illuminate\Cache\Events\CacheHit (164μs)
      • Illuminate\Cache\Events\CacheHit (179μs)
      • Illuminate\Cache\Events\CacheHit (346μs)
      • Illuminate\Cache\Events\CacheHit (257μs)
      • Illuminate\Cache\Events\CacheHit (250μs)
      • Illuminate\Cache\Events\CacheHit (494μs)
      • Illuminate\Cache\Events\CacheHit (341μs)
      • Illuminate\Cache\Events\CacheHit (493μs)
      • Illuminate\Cache\Events\CacheHit (181μs)
      • Illuminate\Cache\Events\CacheHit (200μs)
      • Illuminate\Cache\Events\CacheHit (295μs)
      • Illuminate\Cache\Events\CacheHit (246μs)
      • Illuminate\Cache\Events\CacheHit (169μs)
      • Illuminate\Cache\Events\CacheHit (363μs)
      • Illuminate\Cache\Events\CacheHit (175μs)
      • Illuminate\Cache\Events\CacheHit (320μs)
      • Illuminate\Cache\Events\CacheHit (261μs)
      • Illuminate\Cache\Events\CacheHit (186μs)
      • Illuminate\Cache\Events\CacheHit (177μs)
      • Illuminate\Cache\Events\CacheHit (252μs)
      • Illuminate\Cache\Events\CacheHit (238μs)
      • Illuminate\Cache\Events\CacheHit (182μs)
      • Illuminate\Cache\Events\CacheHit (232μs)
      • Illuminate\Cache\Events\CacheHit (303μs)
      • Illuminate\Cache\Events\CacheHit (350μs)
      • Illuminate\Cache\Events\CacheHit (204μs)
      • Illuminate\Cache\Events\CacheHit (339μs)
      • Illuminate\Cache\Events\CacheHit (640μs)
      • Illuminate\Cache\Events\CacheHit (708μs)
      • Illuminate\Cache\Events\CacheHit (862μs)
      • Illuminate\Cache\Events\CacheHit (191μs)
      • Illuminate\Cache\Events\CacheHit (258μs)
      • Illuminate\Cache\Events\CacheHit (239μs)
      • Illuminate\Cache\Events\CacheHit (258μs)
      • Illuminate\Cache\Events\CacheHit (286μs)
      • Illuminate\Cache\Events\CacheHit (300μs)
      • Illuminate\Cache\Events\CacheHit (169μs)
      • Illuminate\Cache\Events\CacheHit (188μs)
      • Illuminate\Cache\Events\CacheHit (162μs)
      • Illuminate\Cache\Events\CacheHit (191μs)
      • Illuminate\Cache\Events\CacheHit (1.43ms)
      • Illuminate\Cache\Events\CacheHit (257μs)
      • Illuminate\Cache\Events\CacheHit (207μs)
      • Illuminate\Cache\Events\CacheMissed (303μs)
      • Illuminate\Database\Events\StatementPrepared (877μs)
      • Illuminate\Database\Events\QueryExecuted (1.01ms)
      • eloquent.retrieved: App\Models\SubjectCat (63μs)
      • Illuminate\Cache\Events\KeyWritten (437μs)
      • Illuminate\Cache\Events\CacheHit (1.02ms)
      • Illuminate\Cache\Events\CacheHit (308μs)
      • Illuminate\Cache\Events\CacheHit (1.13ms)
      • Illuminate\Cache\Events\CacheHit (266μs)
      • Illuminate\Cache\Events\CacheHit (185μs)
      • Illuminate\Cache\Events\CacheHit (191μs)
      • Illuminate\Cache\Events\CacheHit (164μs)
      • Illuminate\Cache\Events\CacheHit (208μs)
      • Illuminate\Cache\Events\CacheHit (167μs)
      • Illuminate\Cache\Events\CacheHit (241μs)
      • Illuminate\Cache\Events\CacheHit (180μs)
      • Illuminate\Cache\Events\CacheHit (184μs)
      • Illuminate\Cache\Events\CacheHit (161μs)
      • Illuminate\Cache\Events\CacheHit (187μs)
      • Illuminate\Cache\Events\CacheHit (160μs)
      • Illuminate\Cache\Events\CacheHit (454μs)
      • Illuminate\Cache\Events\CacheHit (177μs)
      • creating: site.layouts.app (916μs)
      • composing: site.layouts.app (24μs)
      • creating: components.canonical (532μs)
      • composing: components.canonical (108μs)
      • creating: components.open-graph (214μs)
      • composing: components.open-graph (79μs)
      • creating: site.headers.header (502μs)
      • composing: site.headers.header (74μs)
      • Illuminate\Cache\Events\CacheHit (2.35ms)
      • creating: components.footer (89μs)
      • composing: components.footer (101μs)
      • Illuminate\Cache\Events\CacheHit (1.09ms)
      • Illuminate\Cache\Events\CacheMissed (449μs)
      • Illuminate\Database\Events\StatementPrepared (4.34ms)
      • Illuminate\Database\Events\QueryExecuted (1.21ms)
      • eloquent.retrieved: App\Models\SubjectCat (84μs)
      • Illuminate\Cache\Events\KeyWritten (2.03ms)
      • Illuminate\Cache\Events\CacheHit (890μs)
      • Illuminate\Cache\Events\CacheHit (639μs)
      • Illuminate\Cache\Events\CacheHit (386μs)
      • Illuminate\Cache\Events\CacheHit (226μs)
      • Illuminate\Cache\Events\CacheHit (219μs)
      • Illuminate\Cache\Events\CacheHit (422μs)
      • Illuminate\Cache\Events\CacheHit (362μs)
      • Illuminate\Cache\Events\CacheHit (229μs)
      • Illuminate\Cache\Events\CacheHit (221μs)
      • Illuminate\Cache\Events\CacheHit (292μs)
      • Illuminate\Cache\Events\CacheHit (275μs)
      • Illuminate\Cache\Events\CacheHit (372μs)
      • creating: components.forms.contact-us (243μs)
      • composing: components.forms.contact-us (265μs)
      • creating: components.forms.get-started (409μs)
      • composing: components.forms.get-started (139μs)
      • creating: components.forms.free-tool-download (117μs)
      • composing: components.forms.free-tool-download (134μs)
      • creating: components.forms.claim-free-worksheet (225μs)
      • composing: components.forms.claim-free-worksheet (93μs)
      • creating: components.forms.tutor-subscription-waitlist (115μs)
      • composing: components.forms.tutor-subscription-waitlist (65μs)
      • creating: components.forms.tutor-subscription-join (427μs)
      • composing: components.forms.tutor-subscription-join (73μs)
      • creating: components.forms.tutor-support (223μs)
      • composing: components.forms.tutor-support (77μs)
      • 311 x Illuminate\Cache\Events\CacheHit (22.83%)
        154ms
        20 x Illuminate\Database\Events\StatementPrepared (8.41%)
        56.65ms
        20 x Illuminate\Database\Events\QueryExecuted (7.3%)
        49.17ms
        11 x Illuminate\Cache\Events\CacheMissed (2.97%)
        20.04ms
        11 x Illuminate\Cache\Events\KeyWritten (2.81%)
        18.96ms
        1 x Illuminate\Foundation\Events\LocaleUpdated (0.7%)
        4.70ms
        1 x Illuminate\Database\Events\ConnectionEstablished (0.22%)
        1.50ms
        1 x Illuminate\Routing\Events\Routing (0.21%)
        1.42ms
        12 x eloquent.retrieved: App\Models\SubjectCat (0.21%)
        1.41ms
        1 x creating: homework.show (0.18%)
        1.19ms
        1 x creating: site.layouts.app (0.14%)
        916μs
        7 x eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (0.11%)
        740μs
        1 x composing: components.breadcrumbs (0.09%)
        624μs
        1 x creating: components.canonical (0.08%)
        532μs
        1 x Illuminate\Routing\Events\RouteMatched (0.08%)
        523μs
        1 x creating: site.headers.header (0.07%)
        502μs
        1 x creating: components.forms.tutor-subscription-join (0.06%)
        427μs
        1 x creating: components.forms.get-started (0.06%)
        409μs
        1 x creating: components.breadcrumbs (0.06%)
        402μs
        7 x eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.05%)
        321μs
        2 x eloquent.retrieved: App\Models\Subject (0.05%)
        311μs
        1 x composing: homework.show (0.04%)
        291μs
        1 x eloquent.booting: App\Models\SubjectCat (0.04%)
        278μs
        1 x composing: components.forms.contact-us (0.04%)
        265μs
        1 x eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.04%)
        247μs
        1 x creating: components.forms.contact-us (0.04%)
        243μs
        1 x eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibrary (0.03%)
        229μs
        1 x creating: components.forms.claim-free-worksheet (0.03%)
        225μs
        1 x creating: components.forms.tutor-support (0.03%)
        223μs
        1 x creating: components.open-graph (0.03%)
        214μs
        1 x eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibrary (0.03%)
        206μs
        1 x composing: components.forms.get-started (0.02%)
        139μs
        1 x eloquent.booting: App\Models\Subject (0.02%)
        137μs
        1 x composing: components.forms.free-tool-download (0.02%)
        134μs
        1 x creating: components.forms.free-tool-download (0.02%)
        117μs
        1 x creating: components.forms.tutor-subscription-waitlist (0.02%)
        115μs
        1 x composing: components.canonical (0.02%)
        108μs
        1 x composing: components.footer (0.01%)
        101μs
        1 x composing: components.forms.claim-free-worksheet (0.01%)
        93μs
        1 x creating: components.footer (0.01%)
        89μs
        1 x composing: components.open-graph (0.01%)
        79μs
        1 x composing: components.forms.tutor-support (0.01%)
        77μs
        1 x composing: site.headers.header (0.01%)
        74μs
        1 x composing: components.forms.tutor-subscription-join (0.01%)
        73μs
        1 x eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.01%)
        65μs
        1 x composing: components.forms.tutor-subscription-waitlist (0.01%)
        65μs
        1 x eloquent.booted: App\Models\Subject (0.01%)
        61μs
        1 x eloquent.booted: App\Models\SubjectCat (0.01%)
        42μs
        1 x composing: site.layouts.app (0%)
        24μs
      14 templates were rendered
      • 1x homework.showshow.blade.phpblade
      • 1x components.breadcrumbsbreadcrumbs.blade.phpblade
      • 1x site.layouts.appapp.blade.phpblade
      • 1x components.canonicalcanonical.blade.phpblade
      • 1x components.open-graphopen-graph.blade.phpblade
      • 1x site.headers.headerheader.blade.phpblade
      • 1x components.footerfooter.blade.phpblade
      • 1x components.forms.contact-uscontact-us.blade.phpblade
      • 1x components.forms.get-startedget-started.blade.phpblade
      • 1x components.forms.free-tool-downloadfree-tool-download.blade.phpblade
      • 1x components.forms.claim-free-worksheetclaim-free-worksheet.blade.phpblade
      • 1x components.forms.tutor-subscription-waitlisttutor-subscription-waitlist.blade.phpblade
      • 1x components.forms.tutor-subscription-jointutor-subscription-join.blade.phpblade
      • 1x components.forms.tutor-supporttutor-support.blade.phpblade
      uri
      GET college-homework-library/{category}/{subject}/{id}
      middleware
      web, utm.parameters
      controller
      App\Http\Controllers\HomeworkLibraryController@show
      namespace
      where
      as
      homework.show
      file
      app/Http/Controllers/HomeworkLibraryController.php:79-176
      20 statements were executed, 5 of which were duplicates, 15 unique. Show only duplicated75.16ms
      • Connection Establishedtwenty4_siteHomeworkLibraryController.php#91
        Backtrace
        • 13. app/Http/Controllers/HomeworkLibraryController.php:91
        • 14. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 15. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 16. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 17. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `solutionslibrary` where `status` = 'published' and `price` > 0 and `solutionslibrary`.`id` = '62949' limit 1
        22.84mstwenty4_siteHomeworkLibraryController.php#97
        Bindings
        • 0: published
        • 1: 0
        • 2: 62949
        Backtrace
        • 16. app/Http/Controllers/HomeworkLibraryController.php:97
        • 17. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 18. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 19. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 20. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `subjects` where `subjects`.`id` in (268)
        3.49mstwenty4_siteHomeworkLibraryController.php#97
        Backtrace
        • 21. app/Http/Controllers/HomeworkLibraryController.php:97
        • 22. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 23. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 24. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 25. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` in (62949)
        2.1mstwenty4_siteHomeworkLibraryController.php#97
        Backtrace
        • 21. app/Http/Controllers/HomeworkLibraryController.php:97
        • 22. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 23. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 24. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 25. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `subject_cats` where `subject_cats`.`id` = 34 limit 1
        5.33mstwenty4_siteHomeworkLibrary.php#201
        Bindings
        • 0: 34
        Backtrace
        • 20. app/Models/HomeworkLibrary/HomeworkLibrary.php:201
        • 26. app/Http/Controllers/HomeworkLibraryController.php:105
        • 27. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 28. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 29. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
      • select * from `solutionslibrary` where `id` <> 62949 and `subject` = 268 and `status` = 'published' and `price` > 0 order by RAND() limit 6
        15.37mstwenty4_siteHomeworkLibraryRepository.php#30
        Bindings
        • 0: 62949
        • 1: 268
        • 2: published
        • 3: 0
        Backtrace
        • 14. app/Repositories/HomeworkLibraryRepository.php:30
        • 15. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 16. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 18. app/Repositories/HomeworkLibraryRepository.php:39
        • 19. app/Http/Controllers/HomeworkLibraryController.php:139
      • select * from `subjects` where `subjects`.`id` in (268)
        1mstwenty4_siteHomeworkLibraryRepository.php#30
        Backtrace
        • 19. app/Repositories/HomeworkLibraryRepository.php:30
        • 20. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 21. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 23. app/Repositories/HomeworkLibraryRepository.php:39
        • 24. app/Http/Controllers/HomeworkLibraryController.php:139
      • select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` = 62949 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'question' order by `order` asc, `id` asc
        1.75mstwenty4_siteHomeworkLibrary.php#260
        Bindings
        • 0: 62949
        • 1: question
        Backtrace
        • 15. app/Models/HomeworkLibrary/HomeworkLibrary.php:260
        • 16. app/Transformers/HomeworkLibrary/HomeworkLibraryTransformer.php:58
        • 19. vendor/league/fractal/src/TransformerAbstract.php:128
        • 20. vendor/league/fractal/src/TransformerAbstract.php:107
        • 21. vendor/league/fractal/src/Scope.php:383
      • select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` = 62949 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'teaser' order by `order` asc, `id` asc
        1.61mstwenty4_siteHomeworkLibrary.php#260
        Bindings
        • 0: 62949
        • 1: teaser
        Backtrace
        • 15. app/Models/HomeworkLibrary/HomeworkLibrary.php:260
        • 16. app/Transformers/HomeworkLibrary/HomeworkLibraryTransformer.php:69
        • 19. vendor/league/fractal/src/TransformerAbstract.php:128
        • 20. vendor/league/fractal/src/TransformerAbstract.php:107
        • 21. vendor/league/fractal/src/Scope.php:383
      • select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` = 62949 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'solution' order by `order` asc, `id` asc
        1.46mstwenty4_siteHomeworkLibrary.php#260
        Bindings
        • 0: 62949
        • 1: solution
        Backtrace
        • 15. app/Models/HomeworkLibrary/HomeworkLibrary.php:260
        • 16. app/Transformers/HomeworkLibrary/HomeworkLibraryTransformer.php:80
        • 19. vendor/league/fractal/src/TransformerAbstract.php:128
        • 20. vendor/league/fractal/src/TransformerAbstract.php:107
        • 21. vendor/league/fractal/src/Scope.php:383
      • select * from `subject_cats` where `subject_cats`.`id` = 34 limit 1
        1.27mstwenty4_siteHomeworkLibrary.php#201
        Bindings
        • 0: 34
        Backtrace
        • 20. app/Models/HomeworkLibrary/HomeworkLibrary.php:201
        • 32. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 33. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 34. vendor/livewire/livewire/src/ComponentConcerns/RendersLivewireComponents.php:69
        • 35. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
      • select * from `subject_cats` where `subject_cats`.`id` = 1 limit 1
        2.06mstwenty4_siteSubject.php#100
        Bindings
        • 0: 1
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 3 limit 1
        1.62mstwenty4_siteSubject.php#100
        Bindings
        • 0: 3
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 4 limit 1
        3.04mstwenty4_siteSubject.php#100
        Bindings
        • 0: 4
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 10 limit 1
        1.17mstwenty4_siteSubject.php#100
        Bindings
        • 0: 10
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 33 limit 1
        1.21mstwenty4_siteSubject.php#100
        Bindings
        • 0: 33
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 11 limit 1
        1.32mstwenty4_siteSubject.php#100
        Bindings
        • 0: 11
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 5 limit 1
        1.2mstwenty4_siteSubject.php#100
        Bindings
        • 0: 5
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 34 limit 1
        1.36mstwenty4_siteSubject.php#100
        Bindings
        • 0: 34
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 31 limit 1
        1.15mstwenty4_siteSubject.php#100
        Bindings
        • 0: 31
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 36 limit 1
        4.81mstwenty4_siteSubject.php#100
        Bindings
        • 0: 36
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 28. view::components.footer:170
      App\Models\SubjectCat
      12SubjectCat.php
      App\Models\HomeworkLibrary\HomeworkLibrary
      7HomeworkLibrary.php
      App\Models\HomeworkLibrary\HomeworkLibraryFile
      7HomeworkLibraryFile.php
      App\Models\Subject
      2Subject.php
          _token
          VmpwXFS6UG98KDUBEEMXVPlvKgsd3TUSwoR3FsGI
          utm_source
          direct
          redirectUrl
          /college-homework-library/Physics/Physics-Other/62949
          _previous
          array:1 [ "url" => "https://staging.dev.24houranswers.com/college-homework-library/Physics/Physics...
          _flash
          array:2 [ "old" => [] "new" => [] ]
          PHPDEBUGBAR_STACK_DATA
          []
          path_info
          /college-homework-library/Physics/Physics-Other/62949
          status_code
          200
          
          status_text
          OK
          format
          html
          content_type
          text/html; charset=UTF-8
          request_query
          []
          
          request_request
          []
          
          request_headers
          0 of 0
          array:21 [ "priority" => array:1 [ 0 => "u=0, i" ] "accept-encoding" => array:1 [ 0 => "gzip, deflate, br, zstd" ] "sec-fetch-dest" => array:1 [ 0 => "document" ] "sec-fetch-user" => array:1 [ 0 => "?1" ] "sec-fetch-mode" => array:1 [ 0 => "navigate" ] "sec-fetch-site" => array:1 [ 0 => "none" ] "accept" => array:1 [ 0 => "text/html,application/xhtml+xml,application/xml;q=0.9,image/avif,image/webp,image/apng,*/*;q=0.8,application/signed-exchange;v=b3;q=0.7" ] "user-agent" => array:1 [ 0 => "Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)" ] "upgrade-insecure-requests" => array:1 [ 0 => "1" ] "sec-ch-ua-platform" => array:1 [ 0 => ""Windows"" ] "sec-ch-ua-mobile" => array:1 [ 0 => "?0" ] "sec-ch-ua" => array:1 [ 0 => ""HeadlessChrome";v="129", "Not=A?Brand";v="8", "Chromium";v="129"" ] "cache-control" => array:1 [ 0 => "no-cache" ] "pragma" => array:1 [ 0 => "no-cache" ] "x-amzn-trace-id" => array:1 [ 0 => "Root=1-68071f7b-16d4d1af05215960576a412b" ] "host" => array:1 [ 0 => "staging.dev.24houranswers.com" ] "x-forwarded-port" => array:1 [ 0 => "443" ] "x-forwarded-proto" => array:1 [ 0 => "https" ] "x-forwarded-for" => array:1 [ 0 => "3.22.166.101" ] "content-length" => array:1 [ 0 => "" ] "content-type" => array:1 [ 0 => "" ] ]
          request_cookies
          []
          
          response_headers
          0 of 0
          array:5 [ "content-type" => array:1 [ 0 => "text/html; charset=UTF-8" ] "cache-control" => array:1 [ 0 => "no-cache, private" ] "date" => array:1 [ 0 => "Tue, 22 Apr 2025 04:47:55 GMT" ] "set-cookie" => array:2 [ 0 => "XSRF-TOKEN=eyJpdiI6IldYYmhVcE9ENVlCNVNvZm5xWWJnK3c9PSIsInZhbHVlIjoiV3hsZ1JweUhPaTBCR3V2LzlQSXovc1lUK0FZS2VHZWZnaEFPMmZjU0xwMnY4UXd1Um9VT083L2UyeEJhaWJYNkRBY1luemltUXJsbERSL0g0K2JnaGFCdjhJczNndEZMbjZPd1VBdGU0MENrY0RVTnRVLzFoaWhBS3BMY0hkOW4iLCJtYWMiOiIyMzMyYzNkMTlkNGYwY2EyYmZiM2RhYzBlMmVlZWM2M2EyYjliNTRhMjEyYTNhYmE4MmFhYzc1NzY3ODYwNGVmIiwidGFnIjoiIn0%3D; expires=Tue, 22 Apr 2025 06:47:55 GMT; Max-Age=7200; path=/; domain=.24houranswers.com; samesite=laxXSRF-TOKEN=eyJpdiI6IldYYmhVcE9ENVlCNVNvZm5xWWJnK3c9PSIsInZhbHVlIjoiV3hsZ1JweUhPaTBCR3V2LzlQSXovc1lUK0FZS2VHZWZnaEFPMmZjU0xwMnY4UXd1Um9VT083L2UyeEJhaWJYNkRBY1lue" 1 => "24houranswers_session=eyJpdiI6IlJqTldHMS9ZT1ZrTG10Ny9aajRSZGc9PSIsInZhbHVlIjoiRGpGN3hudWZvN1ptNWs3QTlYSUlUNWh0UkNEVGVMNDhOaHFKR2dlR2ZLWFY1d0dRN0ZZMGFDUHhhcFk1UldsemhZZDFRZUtpYmZnWjNRbXV3dDVmYUVaVmM5K2N1K3YrNnk1QmRYK3hoOGdQc2x3dmtJT0tMZmlMV05odWZMYTQiLCJtYWMiOiI4M2ZmZDgxOTNiMGViNDBkNzMwMjMzMzFhMTU2NjkwOGFlYjRiZjQyNDRiYmFhMjc0Zjc3MWEwYjZkZTEzZGYwIiwidGFnIjoiIn0%3D; expires=Tue, 22 Apr 2025 06:47:55 GMT; Max-Age=7200; path=/; domain=.24houranswers.com; httponly; samesite=lax24houranswers_session=eyJpdiI6IlJqTldHMS9ZT1ZrTG10Ny9aajRSZGc9PSIsInZhbHVlIjoiRGpGN3hudWZvN1ptNWs3QTlYSUlUNWh0UkNEVGVMNDhOaHFKR2dlR2ZLWFY1d0dRN0ZZMGFDUHhhcFk1Ul" ] "Set-Cookie" => array:2 [ 0 => "XSRF-TOKEN=eyJpdiI6IldYYmhVcE9ENVlCNVNvZm5xWWJnK3c9PSIsInZhbHVlIjoiV3hsZ1JweUhPaTBCR3V2LzlQSXovc1lUK0FZS2VHZWZnaEFPMmZjU0xwMnY4UXd1Um9VT083L2UyeEJhaWJYNkRBY1luemltUXJsbERSL0g0K2JnaGFCdjhJczNndEZMbjZPd1VBdGU0MENrY0RVTnRVLzFoaWhBS3BMY0hkOW4iLCJtYWMiOiIyMzMyYzNkMTlkNGYwY2EyYmZiM2RhYzBlMmVlZWM2M2EyYjliNTRhMjEyYTNhYmE4MmFhYzc1NzY3ODYwNGVmIiwidGFnIjoiIn0%3D; expires=Tue, 22-Apr-2025 06:47:55 GMT; domain=.24houranswers.com; path=/XSRF-TOKEN=eyJpdiI6IldYYmhVcE9ENVlCNVNvZm5xWWJnK3c9PSIsInZhbHVlIjoiV3hsZ1JweUhPaTBCR3V2LzlQSXovc1lUK0FZS2VHZWZnaEFPMmZjU0xwMnY4UXd1Um9VT083L2UyeEJhaWJYNkRBY1lue" 1 => "24houranswers_session=eyJpdiI6IlJqTldHMS9ZT1ZrTG10Ny9aajRSZGc9PSIsInZhbHVlIjoiRGpGN3hudWZvN1ptNWs3QTlYSUlUNWh0UkNEVGVMNDhOaHFKR2dlR2ZLWFY1d0dRN0ZZMGFDUHhhcFk1UldsemhZZDFRZUtpYmZnWjNRbXV3dDVmYUVaVmM5K2N1K3YrNnk1QmRYK3hoOGdQc2x3dmtJT0tMZmlMV05odWZMYTQiLCJtYWMiOiI4M2ZmZDgxOTNiMGViNDBkNzMwMjMzMzFhMTU2NjkwOGFlYjRiZjQyNDRiYmFhMjc0Zjc3MWEwYjZkZTEzZGYwIiwidGFnIjoiIn0%3D; expires=Tue, 22-Apr-2025 06:47:55 GMT; domain=.24houranswers.com; path=/; httponly24houranswers_session=eyJpdiI6IlJqTldHMS9ZT1ZrTG10Ny9aajRSZGc9PSIsInZhbHVlIjoiRGpGN3hudWZvN1ptNWs3QTlYSUlUNWh0UkNEVGVMNDhOaHFKR2dlR2ZLWFY1d0dRN0ZZMGFDUHhhcFk1Ul" ] ]
          session_attributes
          0 of 0
          array:6 [ "_token" => "VmpwXFS6UG98KDUBEEMXVPlvKgsd3TUSwoR3FsGI" "utm_source" => "direct" "redirectUrl" => "/college-homework-library/Physics/Physics-Other/62949" "_previous" => array:1 [ "url" => "https://staging.dev.24houranswers.com/college-homework-library/Physics/Physics-Other/62949" ] "_flash" => array:2 [ "old" => [] "new" => [] ] "PHPDEBUGBAR_STACK_DATA" => [] ]