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How to solve for allowed energies with the WKB approximation?

  1. May 4, 2013 #1

    I'm trying to solve for the allowed energies with the WKB approximation of the Schrodinger equation, using the Morse potential.

    So I have (as per equation 35 at http://hitoshi.berkeley.edu/221a/WKB.pdf),

    [itex]\int_a^b \sqrt{2m(E-V(x))}dx=\left(n+\frac{1}{2}\right)\pi\hbar[/itex]

    However, how do I integrate this between the two turning points (those [itex]x[/itex] such that [itex]V(x)=E[/itex]) when they are complex? I would appreciate a reference to any numerical algorithms I could use.

    Thank you!
  2. jcsd
  3. May 5, 2013 #2


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    Can you maybe explain how you got complex coordinates in the first place? Because I thought that those are usually real in QM.
  4. May 22, 2013 #3
    Yes, sorry, I was confused.
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