Introduction To Quantum Mechanics
3rd Edition
ISBN: 9781107189638
Author: Griffiths, David J., Schroeter, Darrell F.
Publisher: Cambridge University Press
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Question
Chapter 11.1, Problem 11.3P
To determine
To solve the given equation for the case of a time-independent perturbation.
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Check out a sample textbook solutionStudents have asked these similar questions
log z = log r + i
is holomorphic in the region r>0 and - < 0 <.
10. Show that
where z = re¹ with - < 0 <
where is the Laplacian
Ә
əz əz
A
= 4
əz əz
dx²
8²
dy²
11. Use Exercise 10 to prove that if f is bolomorphic in the open set , then the
real and imaginary parts of f are harmonic; that is, their Laplacian is zero.
Problem 1.17 A particle is represented (at time=0) by the wave function
A(a²-x²). if-a ≤ x ≤+a.
0,
otherwise.
4(x, 0) = {
(a) Determine the normalization constant A.
(b) What is the expectation value of x (at time t = 0)?
(c) What is the expectation value of p (at time t = 0)? (Note that you cannot
get it from p = md(x)/dt. Why not?)
(d) Find the expectation value of x².
(e) Find the expectation value of p².
Divergence theorem. (a) Use the divergence theorem to prove,
v = -478 (7)
(2.1)
(b) [Problem 1.64, Griffiths] In case you're not persuaded with (a), try replacing r by (r² + e²)2
and watch what happens when ɛ → 0. Specifically, let
1
-V².
4л
1
D(r, ɛ)
(2.2)
p2 + g2
By taking note of the defining conditions of 8°(7) [(1) at r = 0, its value goes to infinity, (2) for
all r + 0, its value is 0, and (3) the integral over all space is 1], demonstrate that 2.2 goes to
8*(F) as ɛ → 0.
Chapter 11 Solutions
Introduction To Quantum Mechanics
Ch. 11.1 - Prob. 11.1PCh. 11.1 - Prob. 11.2PCh. 11.1 - Prob. 11.3PCh. 11.1 - Prob. 11.4PCh. 11.1 - Prob. 11.5PCh. 11.1 - Prob. 11.6PCh. 11.1 - Prob. 11.7PCh. 11.1 - Prob. 11.8PCh. 11.1 - Prob. 11.9PCh. 11.3 - Prob. 11.10P
Ch. 11.3 - Prob. 11.11PCh. 11.3 - Prob. 11.12PCh. 11.3 - Prob. 11.13PCh. 11.3 - Prob. 11.14PCh. 11.3 - Prob. 11.15PCh. 11.3 - Prob. 11.16PCh. 11.4 - Prob. 11.17PCh. 11.5 - Prob. 11.18PCh. 11.5 - Prob. 11.19PCh. 11.5 - Prob. 11.20PCh. 11.5 - Prob. 11.21PCh. 11.5 - Prob. 11.22PCh. 11 - Prob. 11.23PCh. 11 - Prob. 11.24PCh. 11 - Prob. 11.25PCh. 11 - Prob. 11.26PCh. 11 - Prob. 11.27PCh. 11 - Prob. 11.28PCh. 11 - Prob. 11.29PCh. 11 - Prob. 11.30PCh. 11 - Prob. 11.31PCh. 11 - Prob. 11.33PCh. 11 - Prob. 11.35PCh. 11 - Prob. 11.36PCh. 11 - Prob. 11.37P
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