Applied Quantum Mechanics, Second Edition
Using real-world engineering examples to engage the reader, the author of this detailed text makes quantum mechanics accessible and relevant to the engineering student.
TABLE OF CONTENTS Applied Quantum Mechanics, Second Edition
8.6: Example Exercises
8.6 Example Exercises
Exercise 8.1
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A particle of mass m is in a one-dimensional, rectangular potential well for which V( x) = 0 for 0 < x < L and V( x) = ? elsewhere. The particle is initially prepared in the ground state ? 1 with eigenenergy E 1. Then, at time t = 0, the potential is very rapidly changed so that the original wave function remains the same but V( x) = 0 for 0 < x < 2 L and V( x) = ? elsewhere. Find the probability that the particle is in the first, second, third, and fourth excited state of the system when t ? 0.
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Consider the same situation as (a) but for the case in which at time t = 0 the potential is very rapidly changed so that the original wave function remains the same but V( x) = 0 for 0 < x < ?L, where 1 < ? < 5, and V( x) = ? elsewhere. Write a computer program that plots the probability of finding the particle in the ground, first, second, third and fourth excited states of the system as a function of the parameter ?.
Exercise 8.2
The coulomb potential energy in real space between charges e and ? e is
where ?
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