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 6.6, Problem 6.18P
(a)
To determine
Prove that the translation and inversion do not commute.
(b)
To determine
Show that the Eigen state of momentum and its parity are the same energy.
(c)
To determine
Show that the translation operator mixes
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Students have asked these similar questions
Show that if (h|ệh) = (Ôh\h) for all functions h (in Hilbert space),
then (flÔg) = (Ôf\g) for all f and g (i.e., the two definitions of "hermi-
tian"-Equations 3.16 and 3.17-are equivalent). Hint: First let h = f+ 8, and
then let h = f + ig.
(SIÊF) = (Ô ƒIS) for all f(x).
[3.16]
(FIÔg) = (Ô ƒ\g) for all f (x) and all g(x).
[3.17]
b): Consider two identical linear oscillators' having a spring constant k. The interaction
potential is H = Ax|X2, where xi and x2 are the coordinates of the oscillators. Obtain the
energy eigen values.
In terms of the âî and p operators, calculate the following commutation relations. You can assume
h(x) is a fine test function to help facilitate the calculations. Do not include h(x) as part of your answer.
(a)
Calculate [£2,p]).
(b)
Calculate [î, p²].
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
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