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What wave function should I choose for this problem?

  1. Dec 28, 2014 #1
    1. The problem statement, all variables and given/known data
    Show that the operator

    [tex]O = i\frac{d^{3}}{dx^{3}}[/tex]

    has real eigenvalues

    2. Relevant equations
    Differentiate a wave function 3 times

    3. The attempt at a solution
    I know the process of differentiating a wave function (as many times as you like) and it giving the wave function back multiplied the eigen value. But this question seems so general, what wave function should I choose?

    thanks in advance for any pointers
     
  2. jcsd
  3. Dec 28, 2014 #2

    hilbert2

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    Science Advisor
    Gold Member

    The eigenfunctions are linear combinations of functions of form ##e^{kx}##. To give an ansver to the problem, you should explain why ##k## has to be imaginary for this to be an acceptable wave function (if k were real, the eigenvalue would be imaginary).
     
  4. Dec 28, 2014 #3
    that's very helpful, thank you!
     
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