Introduction To Quantum Mechanics
3rd Edition
ISBN: 9781107189638
Author: Griffiths, David J., Schroeter, Darrell F.
Publisher: Cambridge University Press
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Chapter 1.5, Problem 1.8P
To determine
The effect of adding a potential on its wave function and expectation value of a dynamic variable.
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I mean independent of x as well as 1). In classical mechanics this doesn't change
anything, but what about quantum mechanics? Show that the wave function picks
up a time-dependent phase factor: exp(-iVot/ħ). What effect does this have on
the expectation value of a dynamical variable?
Suppose you add a constant Vo to the potential energy (by "constant"
The following problem arises in quantum mechanics (see Chapter 13, Problem 7.21). Find the number of ordered triples of nonnegative integers a, b, c whose sum a+b+c is a given positive integer n. (For example, if n = 2, we could have (a, b, c) = (2, 0, 0) or (0, 2, 0) or (0, 0, 2) or (0, 1, 1) or (1, 0, 1) or (1, 1, 0).) Hint: Show that this is the same as the number of distinguishable distributions of n identical balls in 3 boxes, and follow the method of the diagram in Example 5.
Consider a 1-dimensional quantum system of one particle
Question 01:
in which the particle is under a potential V(x) = mw?a?, with m being the
mass of the particle and w being a parameter (you may take it as angular fre-
quency) with inverse dimension of time. The particle may be found in the region
-0 < x < o.
Varify that the lowest two states of the system are mutually orthonormal.
Chapter 1 Solutions
Introduction To Quantum Mechanics
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