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
Q#10. (a) Show that any component of the momentum operator of a particle is compatible with
its kinetic energy operator.
(b) Show that the momentum operator is compatible with the Hamiltonian operator only if
the potential operator is constant in space coordinates.
Problem 3.7
(a) Suppose that f(x) and g(x) are two eigenfunctions of an operator Q, with
the same eigenvalue q. Show that any linear combination of f and g is itself
an eigenfunction of Q. with eigenvalue q.
(b) Check that f(x) = exp(x) and g(x) = exp(-x) are eigenfunctions of the
operator d?/dx², with the same eigenvalue. Construct two linear combina-
tions of f and g that are orthogonal eigenfunctions on the interval (-1, 1).
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]
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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