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Three dimensional oscillator

  1. Feb 18, 2014 #1
    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. jcsd
  3. Feb 18, 2014 #2
    Hi.
    Is this following a chapter about the variational method?
     
  4. Feb 18, 2014 #3
    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.
     
  5. Feb 18, 2014 #4
    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...
     
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