L, m quantum numbers of 3D oscillator

[yunseok]

Homework Statement

6 degenerate energy states at E=7/2 h-bar w in isotropic 3D harmonic oscillator.
pick one possible state( for example, (nx,ny,nz)=(1,0,1)), and find possible l, m quantum numbers
you may use orthonormality of spherical harmonics[/B]

Homework Equations

pick one possible state( for example, (nx,ny,nz)=(1,0,1)), and find possible l, m quantum numbers[/B]

The Attempt at a Solution

I tried to understand why the question said 'you may pick (1,0,1), and got it.
But I have no idea with orthonormality. What I know about it is just

double integral 0 to pi and 0 to 2pi (Y(l,m), Y(l',m'))sin(theta)d(theta)d(phi) = delta(mm')delta(ll')

sorry for bad notations.

How can I use this property to get quantum number l, m at (nx, ny, nz)=(1,0,1) ?

also, how can I change quantum numbers from carte to polar and from polar to carte

 

[blue_leaf77]

Do you know the functional form of the eigenstate corresponding to (nx,ny,nz)=(1,0,1) in Cartesian coordinate?