Modern Physics, 3rd Edition
3rd Edition
ISBN: 9780534493394
Author: Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Publisher: Cengage Learning
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Chapter 7, Problem 13P
To determine
The expression for the reflection coefficient
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PROBLEM 2. Calculate the probabilities of measurement of different mo-
menta p for a particle with the wave function
(x) = Ceka sin (gx),
%3D
where C is a normalization constant.
Start by defining
1(1) = N1 sin(7r/a)
(1)
b2(x) = N2 sin(2ñr/a)
(2)
for the infinite square well. Fix N1 and N2 so that
%3D
2)
You should find that p(r) is periodic in time. That is p(x, t + T) = p(x,t). Find
that T, and draw p(x) for at t = 0, t = T/4, t = T/2, and T = 3T/4.
PROBLEM 3. Using the variational method, calculate the ground state en-
ergy Eo of a particle in the triangular potential:
U(r) = 0 r 0.
Use the trial function
v(x) = Cx exp(-ar),
where a is a variational parameter and C is a normalization constant to
be found. Compare your result for Eo with the exact solution, Eo
1.856(h? F/m)/3.
Chapter 7 Solutions
Modern Physics, 3rd Edition
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