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Harmonics Oscillator

  1. Apr 25, 2009 #1
    1. The problem statement, all variables and given/known data

    Show:
    [tex] \psi_1=N x e^{-\frac{x^2}{\sigma}} [/tex] is an eigenfunction of the total energy operator(H).

    2. Relevant equations
    psi=N x exp[-x^2/K]


    3. The attempt at a solution
    I plugged in the above to the Schrodinger Equation-time indep. for Harmonic oscillator but I keep getting an x^2 dependence inside the calculation. Do I not plug this in?
     
  2. jcsd
  3. Apr 25, 2009 #2
    oh, I should be putting psi into d^2(psi)/dy^2 + (e-y^2) psi =0 where y=sqrt(mw/h) x. the asymtotic solution: e-->0. This is what is I should plug it into right?
     
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