Quantum Mechanics 3D harmonic oscillator

[sbaseball]

What is the normalized ground-state energy eigenfunction for the three-dimensional harmonic oscillator

V(r) = 1/2 m* ω^2 * r^2

Use separation of varaibles strategy. Express the wave function in spherical coordinates. What is the orbital angualar momentum of the ground state? Explain?

I am having a lot of trouble even knowing where to start. Any help would be appreciated. Thank you

 

[king vitamin]

Have you seen Schrödinger's Equation in spherical coordinates before (e.g., the Hydrogen atom)?

 

[sbaseball]

Yes I have. A long equation with partial derivatives

 

[vela]

The problem tells you what to do. If you don't know what separation of variables is, I'd say start there by reading up about it.

 

[sbaseball]

I use separation of variables with regards to the r component? x^2 + y^2 + z^2 and then use the schrondiger equation and solve it that way? by converting the x y and z component into sperhical coordinates?

 

[genericusrnme]

I use separation of variables with regards to the r component? x^2 + y^2 + z^2 and then use the schrondiger equation and solve it that way? by converting the x y and z component into sperhical coordinates?

nono
Convert everything into spherical polar coordinates first, that wat the r component is just the r component, working with x^2+y^2+z^2 isn't really useful here (the potential is already in given spherical polar coordinates anyway, why convert back to cartesian?)

Once you have done that, schrodingers equation should look something like the laplacian in spherical polar coordinates.
Then you use separation of variables \Psi (r,\theta,\phi)= R(r)Y(\theta,\phi) and go from there

 

[vela]

I use separation of variables with regards to the r component? x^2 + y^2 + z^2 and then use the schrondiger equation and solve it that way? by converting the x y and z component into sperhical coordinates?

It's clear from what you wrote you don't understand what the method of separation of variables is, so I'll repeat my suggestion to read up on it.

Your quantum mechanics textbook should cover how to solve the Schrödinger equation for the hydrogen atom. This problem is very similar to that one.