Is the Classical Electric Potential a Valid Approximation in Quantum Mechanics?

[cragar]

When we setup the Schrödinger equation for the hydrogen atom we use the classical electric potential. It seems that we would need a new potential instead of mixing QM and classical.
Is this just a very good approximation or is there something subtle.

 

[Pengwuino]

When we setup the Schrödinger equation for the hydrogen atom we use the classical electric potential. It seems that we would need a new potential instead of mixing QM and classical.
Is this just a very good approximation or is there something subtle.

It's a very good approximation. For one, relativistic corrections exist (but that's not what you're asking) that come about with the Dirac Equation. As for your question, in what is termed "Second Quantization", the electromagnetic potential can also be quantized. This is the field of Quantum Electrodynamics (QED). It provides the most accurate framework for including the electromagnetic potentials.

 

[cragar]

thanks for your answer. if its not to much trouble how do they correct for relativity in the potential.