How to solve for allowed energies with the WKB approximation?

[Hypercubes]

Hello,

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

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

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

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

Thank you!

 

[CompuChip]

Can you maybe explain how you got complex coordinates in the first place? Because I thought that those are usually real in QM.

 

[Hypercubes]

Yes, sorry, I was confused.