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Eigenvalue Question (p2.14 in Quantum Chemistry and Spectroscopy)

  1. Jan 18, 2012 #1
    function: e^-(x^2/2)
    operator: d^2/dx^2 -x^2

    The answer key says the function is an eigenfunction of the operator with an eigenvalue of -6.

    I can't figure out how to reach this conclusion. Also, Wolfram Alpha says d/dx(d/(dx)e^(-x^2/2)) = e^(-x^2/2) (x^2-1). Isn't this inconsistent with the answer key? Thanks.
  2. jcsd
  3. Jan 18, 2012 #2


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    Homework Helper

    It is an eigenfunction, but with different eigenvalue.

  4. Apr 15, 2012 #3
    guys please help me doing this,
    the operator is given as x+ d/dx
    i have to find the eigenvalue. how to do it?
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