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 3, Problem 3.39P
To determine
The matrix form for x, p and H.
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3.20 Construct the matrix representations of the operators J, and J, for a spin 1 system,
in the J. basis, spanned by the kets |+) = [1,1), 10) = 1,0), and -) = 1,-1). Use
these matrices to find the three analogous eigenstates for each of the two operators
J, and J, in terms of +), 10), and -).
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.
Show that a gaussian psi (x) = e ^(-ax^2) can be an eigenfunction of H(hat) for harmonic oscillator
1. Compute T(hat)*psi
2. Compute Vhat* psi - assume V operator is 1/2w^2x^2
3. Write out Hbar*psi and identify terms so Hber*psi=E*psi is true
4. From cancellation find a
5. insert back a to Schrodinger eq above and find E
Chapter 3 Solutions
Introduction To Quantum Mechanics
Ch. 3.1 - Prob. 3.1PCh. 3.1 - Prob. 3.2PCh. 3.2 - Prob. 3.3PCh. 3.2 - Prob. 3.4PCh. 3.2 - Prob. 3.5PCh. 3.2 - Prob. 3.6PCh. 3.3 - Prob. 3.7PCh. 3.3 - Prob. 3.8PCh. 3.3 - Prob. 3.9PCh. 3.3 - Prob. 3.10P
Ch. 3.4 - Prob. 3.11PCh. 3.4 - Prob. 3.12PCh. 3.4 - Prob. 3.13PCh. 3.5 - Prob. 3.14PCh. 3.5 - Prob. 3.15PCh. 3.5 - Prob. 3.16PCh. 3.5 - Prob. 3.17PCh. 3.5 - Prob. 3.18PCh. 3.5 - Prob. 3.19PCh. 3.5 - Prob. 3.20PCh. 3.5 - Prob. 3.21PCh. 3.5 - Prob. 3.22PCh. 3.6 - Prob. 3.23PCh. 3.6 - Prob. 3.24PCh. 3.6 - Prob. 3.25PCh. 3.6 - Prob. 3.26PCh. 3.6 - Prob. 3.27PCh. 3.6 - Prob. 3.28PCh. 3.6 - Prob. 3.29PCh. 3.6 - Prob. 3.30PCh. 3 - Prob. 3.31PCh. 3 - Prob. 3.32PCh. 3 - Prob. 3.33PCh. 3 - Prob. 3.34PCh. 3 - Prob. 3.35PCh. 3 - Prob. 3.36PCh. 3 - Prob. 3.37PCh. 3 - Prob. 3.38PCh. 3 - Prob. 3.39PCh. 3 - Prob. 3.40PCh. 3 - Prob. 3.41PCh. 3 - Prob. 3.42PCh. 3 - Prob. 3.43PCh. 3 - Prob. 3.44PCh. 3 - Prob. 3.45PCh. 3 - Prob. 3.47PCh. 3 - Prob. 3.48P
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