Fundamentals of Physics Extended (10th Edition)

Published by Wiley
ISBN 10: 1-11823-072-8
ISBN 13: 978-1-11823-072-5

Chapter 39 - More about Matter Waves - Questions - Page 1214: 10b

Answer

In a finite well, the magnitude of the momentum is less than it would be if the potential well were infinite.

Work Step by Step

In a finite well, the matter wave leaks into the walls of the well. However, in an infinite well, the matter wave is restricted by the walls of the well. Therefore, in a finite well, the de Broglie wavelength $\lambda$ is greater than it would be if the potential well were infinite. We can write an expression for the momentum: $\lambda = \frac{h}{p}$ $p = \frac{h}{\lambda}$ Since $\lambda$ is greater in a finite well, then the magnitude of the momentum $p$ is less in a finite well. In a finite well, the magnitude of the momentum is less than it would be if the potential well were infinite.
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