Three Dimensional Anisotropic Harmonic Oscillator An oscillator bas the potential energy function U(x y z) k 1 (x 2 y 2 ) k 2 z 2 where k 1 k 2 This oscillator is called anisotropic because the force constant is not the same in all three coordinate directions (a) Find a general expression for the e...

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Three-Dimensional Anisotropic Harmonic Oscillator An oscillator bas the potential-energy function U(x. y. z) = k 1

Question:

Three-Dimensional Anisotropic Harmonic Oscillator An oscillator bas the potential-energy function U(x. y. z) = ½ k₁(x² + y²) + ½ k₂^’ z² where k₁ > k₂. This oscillator is called anisotropic because the force constant is not the same in all three coordinate directions.

(a) Find a general expression for the energy levels of the oscillator (see Problem 40.53).

(b) From your results in part (a) what are the ground-level and first x-cited-level energies of this oscillator?

(c) How many states (different sets of quantum numbers n_x, n_y, and n_z) are there for the ground level and for the first excited level? Compare to part (c) of Problem 40.53.