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What wave function should I choose for this problem?

  • Thread starter rwooduk
  • Start date
  • #1
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Homework Statement


Show that the operator

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

has real eigenvalues

Homework Equations


Differentiate a wave function 3 times

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
 

Answers and Replies

  • #2
hilbert2
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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).
 
  • #3
747
55
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).
that's very helpful, thank you!
 

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