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Eigenvalue for 1D Quantum Harmonic Oscillator

  1. Feb 3, 2013 #1
    1. The problem statement, all variables and given/known data

    Show that the following is an eigenfunction of [tex]\hat{H}_{QHO}[/tex] and hence find the corresponding eigenvalue:

    [tex]u(q)=A (1-2q^2) e^\frac{-q^2} {2}[/tex]


    2. Relevant equations

    Hamiltonian for 1D QHO of mass m
    [tex]\hat{H}_{QHO} = \frac{\hat{p}^2}{2m} + \frac{1}{2} m \omega^2 x^2[/tex]

    Not sure about any others

    3. The attempt at a solution

    I don't know where to start
     
  2. jcsd
  3. Feb 3, 2013 #2
    What means that a function is an eigen-function of some operator? Doesn't this mean that when you act with that operator on that function, the result will be the original function multiplied by a constant (where this constant is the eigenvalue)?

    So, try to operate with HQHO on u(q) and see what happens!


    (the momentum operator is repsresented by -i[itex]\hbar[/itex]d/dx)
     
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