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Schrodinger equation

  1. Aug 23, 2009 #1
    Hi,

    is this the time independent schrodinger equation for a simple harmonic oscillator?

    [tex]-\frac{1}{2}\frac{d^{2}\psi}{dx^2}+\frac{1}{2}x^{2}\psi(x)=\epsilon\psi(x)[/tex]

    where epsilon is the rescaled energy eigenvalue.
     
    Last edited: Aug 23, 2009
  2. jcsd
  3. Aug 23, 2009 #2
    Yup, in one dimension.
     
  4. Aug 23, 2009 #3
    is it really? because i tried to find out the eigenvalues by integrating with euler's method and i cant find any values for epsilon such that the boundary condition [tex]\psi(\infty)=0[/tex] is satisfied.
     
  5. Aug 23, 2009 #4

    kuruman

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    Maybe your method is flawed. You know what the energy for a harmonic oscillator is. Have you tried to put in that value, say for the ground state, and see whether the boundary condition is satisfied?
     
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