Eigenenergies of finite square well

[secret2]

Is there any website where I can find the analytic form of the eigenenergy of a 1-D finite square well potential?

 

[dextercioby]

I'm sure there is,but don't u have a textbook...?IIRC,there's a nice presentation of this problem in Davydov.

Any QM textbook ought to have finite square well...

Daniel.

 

[jtbell]

Is there any website where I can find the analytic form of the eigenenergy of a 1-D finite square well potential?

There's no explicit analytic expression for the energy eigenvalues of a finite square well. To get them, you have to solve a transcendental equation (two of them actually, one for odd-parity eigenfunctions, one for even-parity). This gives you numeric solutions to whatever precision you need.

Unless of course someone has defined some kind of special function to fill the fill, but I've never heard of any such thing.

Do a Google search for "finite square well" (with the quote marks) and you'll find plenty of Web sites. Some of them probably include the transcendental equations in question.

 

[secret2]

In fact, I am working on a variational method problem. I am asked to prove that any finite square should have at least one bound state. So I plug in a Gaussian trial function to the square well potential. The variational method give neatly V (which is the "depth" of the well). Just want to check if this makes sense.