I Solve Schrodinger Equation for Electrons in Atom: Potential Used?

[Charles Link]

Unfortunately, this is not what was asked by the OP. If you look back at the very first post, the OP explicitly indicated that the starting point of this derivation is the Schrodinger equation.

If the OP had wanted the Bohr-Sommerfield model and the energy quantization from it, this would have been dealt with within the first few post. But noooooo... that is not what he wanted.

This is definitely the case where the eyes are bigger than the stomach.

Zz.

I realize this is not exactly what the OP asked for, but I'm also trying to make sure the OP doesn't lose sight of the basic physics when he finds himself swamped in difficult mathematics. In this instance, I wouldn't even call the Bohr atom a watered-down approach. It is a very important stepping stone that provides a very important part of the foundation. One thing I think the OP is looking for is some useful mathematics, and the Bohr model of the atom provides it. There is no simple way that I know of to learn the more complex models, including the one using the Dirac equation which I never completely understood. (presented in Bjorken and Drell's textbooks).

 

[ZapperZ]

I realize this is not exactly what the OP asked for, but I'm also trying to make sure the OP doesn't lose sight of the basic physics when he finds himself swamped in difficult mathematics. In this instance, I wouldn't even call the Bohr atom a watered-down approach. It is a very important stepping stone that provides a very important part of the foundation. One thing I think the OP is looking for is some useful mathematics, and the Bohr model of the atom provides it. There is no simple way that I know of to learn the more complex models, including the one using the Dirac equation which I never completely understood. (presented in Bjorken and Drell's textbooks).

You are more than welcomed to try and convince the OP that he should learn the simpler case first before attempting what he had been asking.

Zz.

 

[gleem]

@Isaac0427 Here is a link to a similar problem that you have be asking about . http://www.physics.csbsju.edu/QM/square.08.html The round square well. Not a hydrogen atom but is instructive.