Consider the isotropic three-dimensional harmonic oscillator (h0 = h0x h0y h0z , all frequencies equal). Obtain the corrections due to the perturbation.
A) Calculate the first-order correction to the energy.
B) Derive the second-order correction to the wavefunction.
C) Describe the effect of the perturbation on the quantum state.
D) Determine the frequency shift caused by the perturbation.