WKB-Double Potential Well

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Hi,

I need to calculate the energy levels for a generalised potential, which forms a double well, on Matlab as part of a project but I need to understand it analytically first. There doesn't seem to be much information about the topic on the web or in books I checked.

I read the following paper: http://icpr.snu.ac.kr/resource/wop.pdf/J01/2003/042/R06/J012003042R060830.pdf , which I understand till the point where the energy-splitting term has been calculated. But terribly confused after that !

Can anyone please suggest on how to approach the problem and what texts might be helpful?

Cheers!
 

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