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 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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Students have asked these similar questions
Problem
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.
We've looked at the wavefunction for a particle in a box. Soon we will look
at other systems with different constraints and types of motion, which
have a different wavefunction. For example, a particle rotating on a ring
has w(0) =
1
eimo where m= 0, ± 1, + 2,... and ø is the angle
of rotation (analagous to x in the particle in a box problems). For
-n? d?
21 do2
rotational motion the kinetic energy operator is E,
where
I is the moment of inertia (analagous to mass). Use the Schrödinger
equation to calculate the energy of this particle if V = 0.
E=
2m
h?m?
E=
21
m2
E =
21
h?m²
E=
21
Chapter 1 Solutions
Introduction To Quantum Mechanics
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