University Physics Volume 3
17th Edition
ISBN: 9781938168185
Author: William Moebs, Jeff Sanny
Publisher: OpenStax
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Textbook Question
Chapter 7, Problem 30P
A particle with mass m moving along the x-axis and its quantum state is represented by the following wave function:
where a
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Students have asked these similar questions
A hypothetical one dimensional quantum particle has a normalised wave function given by (x) = ax - iß,
where a and 3 are real constants and i = √-1. What is the most likely. x-position, II(x), for the particle to be
found at?
0 11(x) ==
○ II(2) = 0
○ II(r) = 2/
O II(z) =
011(r) =
± √
+√
13
a
You want to determine the possible energy observable values of a particle in a non-
zero potential described by a wave function. Which of the following equations
represents that process?
ħ²
2m
·V² + V| y = 0
+17] 26
οψ
ħ²
[2²] =0
&= 04
2m
– iħ√y = oy
xy = 06
A particle with mass m is moving in three-dimensions under the potential energy U(r), where
r is the radial distance from the origin. The state of the particle is given by the time-independent
wavefunction,
Y(r) = Ce-kr.
Because it is in three dimensions, it is the solution of the following time-independent
Schrodinger equation
dıp
r2
+ U(r)µ(r).
dr
h2 d
EÞ(r) =
2mr2 dr
In addition,
00
1 =
| 4ar?y? (r)dr,
(A(r)) = | 4r²p²(r)A(r)dr.
a. Using the fact that the particle has to be somewhere in space, determine C. Express your
answer in terms of k.
b. Remembering that E is a constant, and the fact that p(r) must satisfy the time-independent
wave equation, what is the energy E of the particle and the potential energy U(r). (As
usual, E and U(r) will be determined up to a constant.) Express your answer in terms of
m, k, and ħ.
Chapter 7 Solutions
University Physics Volume 3
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