A quick physics question. I'm reading an AJP article on finding the bound energies in an asymmetric rectangular potential well. The method it proposes is really interesting and I hope to post a summary of the article soon, but for the moment, I'm stuck on the same step that always seems to stall me with Bohr-Sommerfeld quantization exercises.

Starting with equation 9(picture 1)

taking k approximately equal to the square root of U, we're supposed to arrive at (picture 2)

I can get as close as (picture 3)

but that's it. I'd suspect the article of having a typo, but I know that's the programming equivalent of blaming the compiler, so I'm trying to hold off on that.

Can anyone see where I've gone wrong?

Excerpt from article (picture 4)

**References:**

1. http://ajp.aapt.org/resource/1/ajpias/v69/i11/p1177_s1

doi http://dx.doi.org/10.1119/1.1387043

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