# Three dimensional oscillator

1. Feb 18, 2014

### oomphgalore20

1. The problem statement, all variables and given/known data
Take as a trial wavefunction for the hydrogen atom the 3D oscillator ground state wavefunction
ψ(r) = N exp (-br^2 / 2). Calculate the value of b that gives the best energy and calculate this energy.

2. Relevant equations

Radial part of ∇^2 = 1/r2 (∂/∂r) (r^2 ∂/∂r)

3. The attempt at a solution

I am not sure what best energy is supposed to imply.

2. Feb 18, 2014

### Goddar

Hi.
Is this following a chapter about the variational method?

3. Feb 18, 2014

### oomphgalore20

There is no fixed textbook, so I'm not sure what chapter this precedes or follows; we've covered the simple harmonic oscillator in 1D and went into the variational method while covering perturbation theory. I thought the 3D SHO is an extension of the 1D system, but this 'best energy' is throwing me off.

4. Feb 18, 2014

### Goddar

In a variational method problem it would make sense to take a trial function and vary the parameter b in order to get a higher bound for the ground state energy ("best" energy?), that's why i'm asking. i can't think of another meaning in the context you're giving...