Introduction To Quantum Mechanics
Introduction To Quantum Mechanics
3rd Edition
ISBN: 9781107189638
Author: Griffiths, David J., Schroeter, Darrell F.
Publisher: Cambridge University Press
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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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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.
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