I I want to read about the electron nucleus interaction

[gnnmartin]

My unreliable memory is that although Schrödinger's equation treats the interaction between an electron and the nucleus as unquantised, it is more generally thought to be mediated by an exchange of quanta between electron and nucleus. I want to check on this and get a better understanding. Can anyone please point me at something that covers this, preferably online? And if I am wrong about the exchange of quanta, please let me know!

 

[hilbert2]

Here's one article about that subject, but I don't have the knowledge base to evaluate how good it is: http://www.actaphys.uj.edu.pl/fulltext?series=Reg&vol=48&page=2183

In short, the idea is to add radiative corrections to the semiclassical model where the nucleus and electron create Coulomb potentials proportional to $1/r$ around them. This leads to many kinds of things, such as formation of electron-positron or even muon-antimuon pairs, that affect the ground state energy of hydrogen by small amount.

 

[gnnmartin]

Here's one article about that subject, but I don't have the knowledge base to evaluate how good it is: http://www.actaphys.uj.edu.pl/fulltext?series=Reg&vol=48&page=2183

In short, the idea is to add radiative corrections to the semiclassical model where the nucleus and electron create Coulomb potentials proportional to $1/r$ around them. This leads to many kinds of things, such as formation of electron-positron or even muon-antimuon pairs, that affect the ground state energy of hydrogen by small amount.

Thanks. On a quick read I think that that is too advanced for my purpose: if I follow it correctly, it assume a quantised model and describes a refinement. It does make me think I should re-read QED: I read it ages ago and had remembered it as describing EM radiation in free space, but perhaps it covers nucleus/electron interaction.

 

[hilbert2]

Thanks. On a quick read I think that that is too advanced for my purpose: if I follow it correctly, it assume a quantised model and describes a refinement. It does make me think I should re-read QED: I read it ages ago and had remembered it as describing EM radiation in free space, but perhaps it covers nucleus/electron interaction.

The problem of free waves is the simplest one, as the normal modes of the field behave like independent harmonic oscillators. When there's a Dirac field of fermions (electrons, muons, etc..) interacting with the EM field, it becomes a field system with nonlinear equations of motion and can't be solved exactly even if treated as a classical mechanics system. Therefore the perturbation theory with Feynman diagrams is used. Then you can deduce things like that the production of a muon-antimuon pair is much less likely than the production of an electron-positron pair, and that it is purely a result of the larger mass of a muon.

 

[A. Neumaier]

My unreliable memory is that although Schrödinger's equation treats the interaction between an electron and the nucleus as unquantised

No. What you refer to is already an approximation, called the Born-Oppenheimer approximation. See the Wikipedia article https://en.wikipedia.org/wiki/Born-Oppenheimer_approximation for a derivation of the latter from a full quantum Hamiltonian for the combined motion of electrons and nuclei.