Stationary Orbits, Are they Real or just Idilization?

[TMSxPhyFor]

Hi, I raised this question in another forum but get no satisfactory answer, so hope will get something new here...

Stationary orbits of atoms are based on variable separation (time and spatial) of usual Schrödinger equation when Hamiltonian is time independent, and we get eigenvalues for energies that has been proved experementaly by Hertz a long time ago, and basically they are stationary because by this separation we get what callet dynamical phase e^{-iEt/h} that will disapear in propability and current due to terms like \psi^{*}\psi.

What I can't figure out, is that strictly speaking, the Hamiltonian of even simple atoms like Hydrogen is not really time independent (or I'm wrong?), the proton in the nuclei is bouncing (even in vacuum) and the EM field not static at all, and there is vacuum fluctuations that comes from QEM, and I read that when Solid State physicists modelling molecules they never assume any stationary states (or stationary eigenstate), and all wave functions are always time dependent.

So my question is how all those things are really fit together and if Stationarity is just and idealization or they really exists (up to a very accurate and careful treatment) even so Hamiltonian is not time independent?

 

[mfb]

the proton in the nuclei is bouncing (even in vacuum) and the EM field not static at all, and there is vacuum fluctuations that comes from QEM

All those effects change the energy levels, but the underlying Hamiltonian (of quantum electrodynamics and quantum chromodynamics, if you like) is still time-invariant - it is just more complicated.

Solid state physics is different, you have many other atoms influencing your atom, and solid objects are usually not at absolute zero temperature.

 

[Phy_enthusiast]

stationary here does not mean that they are still or something, stationary means that they are non radiating, it is the very base of quantum mechanics in atomic world...

 

[TMSxPhyFor]

@Phy_enthusiast I know that, it's not my point.
@mfb Can you please show in more detail how the underling Hamiltonian will still be time invariant? that what I can't figure out!

 

[mfb]

@TMSxPhyFor: Quantum field theory is described via Lagrangians, but that should not make a fundamental difference.
The basic laws of physics are time-invariant in the Standard Model, and bound states in the ground-state are "just" energy eigenstates of that.

 

[TMSxPhyFor]

@mfb oh thank you , I think now I understand what I miss, It's time invariance...