System with big number of particles

[lokofer]

System with "big" number of particles..

Let's suppose we have a Hamiltonian of the form:

$$H(q_1 ,q_2 ,q_3,..., q_N , p_1,p_2 ,p_3 , ..., p_N ) \Phi (q_1 ,q_2 ,q_3,..., q_N) = E_{n} \Phi (q_1 ,q_2 ,q_3,..., q_N )$$

but the problem is that N is very "big" , let's say $$N \rightarrow \infty$$ , so to solve the Schrowedinguer equation becomes a very difficult task... is there a method to deal with this problem?...when you have for example a big number of particles inside a box (gas and similar) to solve SE and get the "Energies" and "Wave functions"?

 

[ZapperZ]

This is why there is such a subject matter called "Many-Body Physics", where the ground state Hamiltonian is a many-body system.

You probably want to start by looking up Landau's Fermi Liquid Theory.

Zz.

 

[lokofer]

- Yes, probably..although it was more familiar for me the concept of "Density Functional Theory"...although i have watched it in "wikipedia"...but understand hardly nothing.

 

[lalbatros]

lokofer,

This is also the topic of Statistical Physics!
A book by https://www.amazon.com/gp/product/0894645242/?tag=pfamazon01-20 really starts from the first chapters with this full expression!
Unfortunately, it is out of print.
I don't know of an equivalent, but there should be some.
Maybe you can find Balescu in your library.

Michel