Hydrogen atom solution (split from comparison to Balmer data)

[Enthalpy]

For my personal information please:

 

A part of the electron's and proton's masses result from their electric field. When the electron and proton are close to an other, the electrostatic attraction reduce their energy (twice as much as the kinetic energy increases the electron's mass+energy).

 

Must this energy change be included in the electron's mass to compute the orbitals?

 

Also: this energy change isn't necessarily located at the particles (...with all subtleties associated with a particle position). This energy change is rather everywhere around the proton and the electron, where the square field (E_p+E_e)² differs from E_p²+E_e². Because this energy change can be located elsewhere than the electron's rest mass, its contribution to inertia may not be proportional to the mass+energy change (nor to half the change).

 

Is that included in models for the hydrogen atom? And does it make any sense?

 

Thanks!

[swansont]

The Hamiltonian has an interaction term which would account for any change in energy in having a bound system. The masses you use are the rest masses.

[sb635]

For my personal information please:

 

A part of the electron's and proton's masses result from their electric field. When the electron and proton are close to an other, the electrostatic attraction reduce their energy (twice as much as the kinetic energy increases the electron's mass+energy).

 

Must this energy change be included in the electron's mass to compute the orbitals?

 

Also: this energy change isn't necessarily located at the particles (...with all subtleties associated with a particle position). This energy change is rather everywhere around the proton and the electron, where the square field (E_p+E_e)² differs from E_p²+E_e². Because this energy change can be located elsewhere than the electron's rest mass, its contribution to inertia may not be proportional to the mass+energy change (nor to half the change).

 

Is that included in models for the hydrogen atom? And does it make any sense?

 

Thanks!

 

The masses of the electron and the proton's quarks are theoretically represented now, I suppose, by some type of Higgs mechanism, using the Higgs boson as the virtual field particle.

 

In the hydrogen models I have used, the reduced rest mass of the electron enters the equations, and then gets time dilated (made bigger) in relativistic theory. This increase in mass contributes partly to the increase in the attractive binding energy. The classically-deterministic relativistic energy then gets "blurred" when all of the probabilistic aspects of QM are incorporated, usually as energy perturbations (such as the Darwin term and QED effects). Given Einstein's E = mc², each of these energy perturbations (which include the "non-local" aspects of the electron) could be transformed into some type of "mass perturbation" based equation, but you would then not include the energy perturbations. Just stopping at energy perturbations incorporating the electron's "non-locality," I think answers your question as yes.