A slightly anisotropic three-dimensional harmonic oscillator has z x = y . A

A slightly anisotropic three-dimensional harmonic oscillator has ω_z ≈ ω_x = ω_y. A charged particle moves in the field of this oscillator and is at the same time exposed to a uniform magnetic field in the x-direction. Assuming that the Zeeman splitting is comparable to the splitting produced by the anisotropy, but small compared to h̄ω, calculate to first order the energies of the components of the first excited state. Discuss various limiting cases.