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System with big number of particles

  1. Aug 28, 2006 #1
    System with "big" number of particles..

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

    [tex] 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 ) [/tex]

    but the problem is that N is very "big" , let's say [tex] N \rightarrow \infty [/tex] , 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"?
     
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  3. Aug 28, 2006 #2

    ZapperZ

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    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.
     
  4. Aug 28, 2006 #3
    - 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.
     
  5. Aug 28, 2006 #4
    lokofer,

    This is also the topic of Statistical Physics!
    A book by Balescu (1991) 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
     
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