4.7 Consider an infinite square-well potential of width a, but with the coordinate system shifted so that the infinite potential barriers lie at x = a/2 and x = a/2 (see diagram): V(x) x = =-= x = 12 X (a) Solve the Schrödinger equation for this case to calculate the normalized wave functions Un(x) and the corresponding energies En. (b) Explain why you get the same energies as for the square well between x = 0 and x = a, but a different set of wave functions.
4.7 Consider an infinite square-well potential of width a, but with the coordinate system shifted so that the infinite potential barriers lie at x = a/2 and x = a/2 (see diagram): V(x) x = =-= x = 12 X (a) Solve the Schrödinger equation for this case to calculate the normalized wave functions Un(x) and the corresponding energies En. (b) Explain why you get the same energies as for the square well between x = 0 and x = a, but a different set of wave functions.
Modern Physics
3rd Edition
ISBN:9781111794378
Author:Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Publisher:Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Chapter6: Quantum Mechanics In One Dimension
Section: Chapter Questions
Problem 16P
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Transcribed Image Text:4.7 Consider an infinite square-well potential of width a, but with the
coordinate system shifted so that the infinite potential barriers lie
at x = a/2 and x = a/2 (see diagram):
V(x)
x =
=-=
x =
12
X
(a) Solve the Schrödinger equation for this case to calculate the
normalized wave functions Un(x) and the corresponding energies
En.
(b) Explain why you get the same energies as for the square well
between x = 0 and x = a, but a different set of wave functions.
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