Three-Dimensional Anisotropic Harmonic Oscillator An oscillator bas the potential-energy function U(x. y. z) = k1(x2 +

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 nx, ny, and nz) are there for the ground level and for the first excited level? Compare to part (c) of Problem 40.53.