Introduction To Quantum Mechanics
3rd Edition
ISBN: 9781107189638
Author: Griffiths, David J., Schroeter, Darrell F.
Publisher: Cambridge University Press
expand_more
expand_more
format_list_bulleted
Question
Chapter 6.2, Problem 6.2P
To determine
Prove that
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
Problem One
1. Show that [L.Pz] = 0.
2. Show that the eigenvalue of
operator is mh, where m is an
integer.
Suppose I have an operator A, and I discover that Â(2²) = 5 sinx and Â(sin x) = 5x².
(a) Find Â(2² - sin x)
(b) Name one eigenfunction
and one eigenvalue of A.
2 ô
Consider operator O
1
and function R(1r)= e-b". What must be the
value of constant b for this function to be an eigenfunction of the operator? In other
words, find such value of the parameter b that
Oe br = E e-br
E is the eigenvalue. Also, find the eigenvalue E.
where
Chapter 6 Solutions
Introduction To Quantum Mechanics
Ch. 6.1 - Prob. 6.1PCh. 6.2 - Prob. 6.2PCh. 6.2 - Prob. 6.3PCh. 6.2 - Prob. 6.4PCh. 6.2 - Prob. 6.5PCh. 6.2 - Prob. 6.7PCh. 6.4 - Prob. 6.8PCh. 6.4 - Prob. 6.9PCh. 6.4 - Prob. 6.10PCh. 6.4 - Prob. 6.11P
Ch. 6.4 - Prob. 6.12PCh. 6.4 - Prob. 6.13PCh. 6.5 - Prob. 6.14PCh. 6.5 - Prob. 6.15PCh. 6.5 - Prob. 6.16PCh. 6.5 - Prob. 6.17PCh. 6.6 - Prob. 6.18PCh. 6.6 - Prob. 6.19PCh. 6.7 - Prob. 6.20PCh. 6.7 - Prob. 6.21PCh. 6.7 - Prob. 6.22PCh. 6.7 - Prob. 6.23PCh. 6.7 - Prob. 6.25PCh. 6.8 - Prob. 6.26PCh. 6.8 - Prob. 6.27PCh. 6.8 - Prob. 6.28PCh. 6.8 - Prob. 6.30PCh. 6 - Prob. 6.31PCh. 6 - Prob. 6.32PCh. 6 - Prob. 6.34PCh. 6 - Prob. 6.35PCh. 6 - Prob. 6.36PCh. 6 - Prob. 6.37P
Knowledge Booster
Similar questions
- Problem 3.7 (a) Suppose that f(x) and g(x) are two eigenfunctions of an operator Q, with the same eigenvalue q. Show that any linear combination of f and g is itself an eigenfunction of Q. with eigenvalue q. (b) Check that f(x) = exp(x) and g(x) = exp(-x) are eigenfunctions of the operator d?/dx², with the same eigenvalue. Construct two linear combina- tions of f and g that are orthogonal eigenfunctions on the interval (-1, 1).arrow_forwardHow do I demonstrate a function is a Hermitian operator? That is my biggest question. If I am understanding well, I need to show that A is a Hermitian operator to get started on this problem. Please help.arrow_forwardExample 3: Prove that, the function Y(x) = Ae¬ax is an eigen function of the operator F d? 2 d +- dx? 2a %3D x dx Where A, a are constantarrow_forward
- WOw  is a Hermitian operator. lµ) is an eigenvector to Å with „cnvalue 1. [ø) is also an eigenvector with eigenvalue µ. Both |4) and lø) are normalized. µ # 1. Compute the following: a. ¡µ) = 4 > AY b. (plå = = 1 FOperty of Hermation Cvator ofe. Compute (9|Ã\µ} – (w\Â\µ) to show that |b) and |9) are orthogonal to each other. 入# MAPN>-0arrow_forward1. Given that x(t) the coordinate operator for a free particle in one dimension. Evaluate [x(t), x(0)] and comment on your result.arrow_forwardSuppose that you have three vectors: fi (x) = 1, f2 (x) = x quadratic functions with the inner product: (f; | f;) = [° fi (x) f; (x) e¯ªdx. Suppose we have a derivative operator D = . What is (f3 |D| f2) =? 1, and f3 (x) =; (x² – 4x + 2), that make up an orthonormal basis spanning the real vector space of - dx 1 5/8 -3/4arrow_forward
- Let V = (xy, xy, (x−y)z). V is solenoidal. Use the homotopy or cone operator method to find a vector potential for it. Is your answer unique? If not, what is the most general vector potential for V?arrow_forwardSuppose that A is a covector field, and consider the object Fμ = 0μA, O₂ A₁. (a) Show explicitly that F is a tensor, that is, show that it transforms appropriately under a coordinate transformation. (b) Show that the definition F = V₁A₂-V₂A, which uses the covariant derivative, is equiv- alent to the definition above.arrow_forwarda2 Laplacian operator 72 = ax? ay? T əz2 in spherical polar coordinates is given by az? p² = () 1 a 1 1 a2 r2 sin e ae sin 0-) is an eigenfunction of the Laplacian operator and find the +- r2 sin 0 a0 r2 ar ar. r2 sin? 0 a20 sin 0 sin o Show that function r2 corresponding eigenvalue.arrow_forward
- For a particle moving in one dimension, show that the operator ?̂?̂ is NOT Hermitian. Construct an operator which corresponds to this physical observable product and is Hermitian. ? and ? are position and momentumof the particle.arrow_forwardPROBLEM 1. Consider two Hermitian operators A and B defined by the matrices: iv 0 a 0 0 0 b 0 0 0 -iv 0 where a, b, c, u, and v are real constants. 1. Is the product A B a Hermitian operator? 2. Do  and B commute? 3. What are the relations between a, b, c, u and v for which the answer to the questions 1 and 2 is yes?arrow_forwardShow that projection operators are idempotent: P2 = P. Determine the eigenvalues of P, and characterize its eigenvectors.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- College PhysicsPhysicsISBN:9781305952300Author:Raymond A. Serway, Chris VuillePublisher:Cengage LearningUniversity Physics (14th Edition)PhysicsISBN:9780133969290Author:Hugh D. Young, Roger A. FreedmanPublisher:PEARSONIntroduction To Quantum MechanicsPhysicsISBN:9781107189638Author:Griffiths, David J., Schroeter, Darrell F.Publisher:Cambridge University Press
- Physics for Scientists and EngineersPhysicsISBN:9781337553278Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningLecture- Tutorials for Introductory AstronomyPhysicsISBN:9780321820464Author:Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina BrissendenPublisher:Addison-WesleyCollege Physics: A Strategic Approach (4th Editio...PhysicsISBN:9780134609034Author:Randall D. Knight (Professor Emeritus), Brian Jones, Stuart FieldPublisher:PEARSON
College Physics
Physics
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Cengage Learning
University Physics (14th Edition)
Physics
ISBN:9780133969290
Author:Hugh D. Young, Roger A. Freedman
Publisher:PEARSON
Introduction To Quantum Mechanics
Physics
ISBN:9781107189638
Author:Griffiths, David J., Schroeter, Darrell F.
Publisher:Cambridge University Press
Physics for Scientists and Engineers
Physics
ISBN:9781337553278
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Lecture- Tutorials for Introductory Astronomy
Physics
ISBN:9780321820464
Author:Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina Brissenden
Publisher:Addison-Wesley
College Physics: A Strategic Approach (4th Editio...
Physics
ISBN:9780134609034
Author:Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:PEARSON