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 7, Problem 7.36P
(a)
To determine
The effect of the perturbation
(b)
To determine
The effect of the perturbation
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Students have asked these similar questions
Problem 3.36. Consider an Einstein solid for which both N and q are much
greater than 1. Think of each oscillator as a separate "particle."
(a) Show that the chemical potential is
N+
- kT ln
N
(b) Discuss this result in the limits N > q and N « q, concentrating on the
question of how much S increases when another particle carrying no energy
is added to the system. Does the formula make intuitive sense?
Problem #1
(Problem 5.3 in book). Come up with a function for A (the Helmholtz free energy) and
derive the differential form that reveals A as a potential:
dA < -SdT – pdV [Eqn 5.20]
2.4.
A particle moves in an infinite cubic potential well described by:
V (x1, x2) = {00
12=
if 0 ≤ x1, x2 a
otherwise
1/2(+1)
(a) Write down the exact energy and wave-function of the ground state.
(2)
(b) Write down the exact energy and wavefunction of the first excited states and specify their
degeneracies.
Now add the following perturbation to the infinite cubic well:
H' = 18(x₁-x2)
(c) Calculate the ground state energy to the first order correction.
(5)
(d) Calculate the energy of the first order correction to the first excited degenerated state.
(3)
(e) Calculate the energy of the first order correction to the second non-degenerate excited
state.
(3)
(f) Use degenerate perturbation theory to determine the first-order correction to the two initially
degenerate eigenvalues (energies).
(3)
Chapter 7 Solutions
Introduction To Quantum Mechanics
Ch. 7.1 - Prob. 7.1PCh. 7.1 - Prob. 7.2PCh. 7.1 - Prob. 7.3PCh. 7.1 - Prob. 7.4PCh. 7.1 - Prob. 7.5PCh. 7.1 - Prob. 7.6PCh. 7.2 - Prob. 7.8PCh. 7.2 - Prob. 7.9PCh. 7.2 - Prob. 7.10PCh. 7.2 - Prob. 7.11P
Ch. 7.2 - Prob. 7.12PCh. 7.2 - Prob. 7.13PCh. 7.3 - Prob. 7.15PCh. 7.3 - Prob. 7.16PCh. 7.3 - Prob. 7.17PCh. 7.3 - Prob. 7.18PCh. 7.3 - Prob. 7.19PCh. 7.3 - Prob. 7.20PCh. 7.3 - Prob. 7.21PCh. 7.3 - Prob. 7.22PCh. 7.4 - Prob. 7.23PCh. 7.4 - Prob. 7.24PCh. 7.4 - Prob. 7.25PCh. 7.4 - Prob. 7.26PCh. 7.4 - Prob. 7.27PCh. 7.4 - Prob. 7.28PCh. 7.4 - Prob. 7.29PCh. 7.5 - Prob. 7.31PCh. 7.5 - Prob. 7.32PCh. 7 - Prob. 7.33PCh. 7 - Prob. 7.34PCh. 7 - Prob. 7.35PCh. 7 - Prob. 7.36PCh. 7 - Prob. 7.37PCh. 7 - Prob. 7.38PCh. 7 - Prob. 7.39PCh. 7 - Prob. 7.40PCh. 7 - Prob. 7.42PCh. 7 - Prob. 7.43PCh. 7 - Prob. 7.44PCh. 7 - Prob. 7.45PCh. 7 - Prob. 7.46PCh. 7 - Prob. 7.47PCh. 7 - Prob. 7.49PCh. 7 - Prob. 7.50PCh. 7 - Prob. 7.51PCh. 7 - Prob. 7.52PCh. 7 - Prob. 7.54PCh. 7 - Prob. 7.56PCh. 7 - Prob. 7.57P
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