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Homework Help: Wave function

  1. Feb 26, 2006 #1
    In a region of space, a particle has a wave function given by [tex] \psi(x) = A\exp(\frac{-x^2}{2L^2}})[/tex] and energy [tex] E = \frac{\hbar^2}{2mL^2} [/tex]

    Find the potential energy as a function of x.

    Do I plug these into the time independent wave equation and solve for U(x) ? If so, I don't see what exactly I'm supposed to do with the energy, E. There is already a similar term in the wave equation.
     
    Last edited: Feb 26, 2006
  2. jcsd
  3. Feb 26, 2006 #2
    [tex]-\frac{\hbar^2}{2m}\frac{d^2}{dx^2} \psi(x) + U(x) \psi (x) = E \psi(x)[/tex].
    Plug in what you know, take the derivative and solve for U(x).

    -Dan
     
  4. Feb 26, 2006 #3
    Ok I was thinking of the time-dependent wave equation.
     
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