Exercise 6.4 Consider an anisotropic three-dimensional harmonic oscillator potential V (x, y, z) = = m(w² x² + w} y² +w? z²). (a) Evaluate the energy levels in terms of @x, @y, and wz.
Exercise 6.4 Consider an anisotropic three-dimensional harmonic oscillator potential V (x, y, z) = = m(w² x² + w} y² +w? z²). (a) Evaluate the energy levels in terms of @x, @y, and wz.
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![Exercise 6.4
Consider an anisotropic three-dimensional harmonic oscillator potential
acy
= { m (w² x ² + w} y² + w? 2²).
V (x, y, z) = = m(o² x² +
@z.
(a) Evaluate the energy levels in terms of wx, @y, and
(b) Calculate [Ĥ, Î₂]. Do you expect the wave functions to be eigenfunctions of 1²?
(c) Find the three lowest levels for the case @x = @y= = 2002/3, and determine the degener-
of each level.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb5e7f421-4fd8-49d8-b638-131a56945312%2Fe1a11bcb-76f1-4ec7-be62-02dc8ee9578c%2Fyxyedl_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Exercise 6.4
Consider an anisotropic three-dimensional harmonic oscillator potential
acy
= { m (w² x ² + w} y² + w? 2²).
V (x, y, z) = = m(o² x² +
@z.
(a) Evaluate the energy levels in terms of wx, @y, and
(b) Calculate [Ĥ, Î₂]. Do you expect the wave functions to be eigenfunctions of 1²?
(c) Find the three lowest levels for the case @x = @y= = 2002/3, and determine the degener-
of each level.
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