# Difference of Hydrogen Hamiltonian with relative mass particles

Tags:
1. Sep 25, 2015

### Abigale

Hi guys,
I consider the qm-derivation of the electronic states of hydrogen.

There are two different derivations (I consider only the coulomb-force):

1) the proton is very heavy, so one can neglect the movement
2) the proton moves a little bit, so one uses the relative mass $\mu$

The derivation for the 1) case is easy.

Where is the physical difference at the end of the calculations for case 1) or 2)?
Do both Hamiltonians lead to the same result?

Thank you very much!!!
Greez Abby

2. Sep 25, 2015

### Orodruin

Staff Emeritus
The derivations are completely analogous. The one using the reduced mass is more accurate since it takes the proton into account in terms of movement. The difference is miniscule as the proton is much much heavier than the electron.

3. Sep 25, 2015

### Staff: Mentor

To quantify miniscule: the proton mass is about 1840 times the electron mass, so all energy levels shift by about 1/1840 of their energy.
Certainly important if you want to do precision spectroscopy, irrelevant if you want to know if the emission will be blue or red.

Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook