Finite-Temperature Schrödinger's equation

[Gavroy]

hi,

i am interested in solutions to the finite-temperature schrödinger's equation for the hydrogen atom. does anybody know whether there are such?

or does anybody of you know whether there is a possiblity to use something like pertubation theory to calculate the new energy-levels of the hydrogen atom at some temperature?

 

[alxm]

What "new" energy levels? The states themselves don't change with temperature.

 

[Gavroy]

are you sure? then why do they invent this new formula.
http://arxiv.org/PS_cache/arxiv/pdf/1005/1005.2751v3.pdf" (23).
does a new term in the hamiltonian not result in new energy levels?

or let me ask it in a different way: what exactly happens when a hydrogen atom is at temperature T and how can i describe this state(or this fluctuation, whatever it is) mathematically?

 

[alxm]

are you sure? then why do they invent this new formula.

Yes I'm sure. That doesn't show otherwise either. A more important question to Why did they invent it:
Where/when has anyone used it? I do actual finite temperature calculations on atoms and molecules all the time, and I certainly haven't either seen it or needed it.

does a new term in the hamiltonian not result in new energy levels?

That's not the Hamiltonian of a single atom or a single particle. You're comparing apples to oranges.

or let me ask it in a different way: what exactly happens when a hydrogen atom is at temperature T and how can i describe this state(or this fluctuation, whatever it is) mathematically?

Create a partition function. Don't you know statistical thermodynamics at all?

 

[Gavroy]

Create a partition function. Don't you know statistical thermodynamics at all?

no, up to now, i was only concerned with mechanics, classical field theory and qm...

actually, it is completely new to me to use statistical mechanics in hydrogen atoms, that have discrete energy levels. how does statistical mechanics work with quantum mechanics?

if it is not too demending, it would be great if you could write down the correct function that gives me the probability for hydrogen atoms at a finite temperature or you could give me a link, where they deal with this problem.


thanks for your help