Optimizing Energy of Hydrogen Atom with 3D Oscillator Wavefunction

[oomphgalore20]

Homework Statement

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.

Homework Equations

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

The Attempt at a Solution

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

 

[Goddar]

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

 

[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.

 

[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...