How Do Eigenvalues of a Three-Dimensional Harmonic Oscillator Arise?

[shally]

Homework Statement

Kindly look at the attachment for the statement.

Homework Equations

L^2 (psi) = E (psi)

The Attempt at a Solution

For Part B,
I wrote Lx, Ly, Lz in operator form. Thus I get L^2. L^2 (psi) = E (psi)
psi = E^-alpha.r^2/2
So I get energy eigenvalue 2 h cross square (option 2).


Kindly help with Part A

 

[ehild]

The Hamiltonian is the sum of those of three independent linear oscillators. The wavefunction is of the form Ψ(x,y,z)=φ(x)φ(y)φ(z), where φ is the linear-oscillator wavefunction, with eigenvalues (hcross)ω(v+1/2); v=0,1,2,... What are the eigenvalues of the three dimensional oscillator then?

ehild