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Analogues between QM- and CM N-body problem

  1. Jun 25, 2015 #1
    In CM general formulation of N-body problem is:
    [itex]x(N;D;T) = \iint \sum_{n=0}^{N_{max}} (\frac {(x(N;D;t)-x(n;D;t))*(m_N*m_n*G+q_N*q_n/(4*π*ε_0))}{(\sum_{d=0}^{D_{max}}((x(N;d;t)-x(n;d;t))^2))^{3/2}*m_N}) \, dt^2[/itex]

    Where x(N;D;T) is D´th coordinate of N´th body at time T.
    But to get equation of motion you need more information for example: speed and velocity of all bodies at given time.

    Is it analogues in QM where general formulation of N-body problem is:
    [itex]U_{System Potential Energy}(r_1,r_2,r_3,...,r_n,t)-\sum_{n=1}^{n_{max}}(\sum_{d=0}^{d_{max}}(\frac{d^2Ψ(r_1,r_2,r_3,...,r_n,t)}{dx_n^2})*\frac{ħ^2}{m_n})=i*ħ \frac{dΨ(r_1,r_2,r_3,...,r_n,t)}{dt}[/itex]
    And to get wave function ψ we also need more information? What information could it be?
    Could tihis information be function [itex]f(r_1,r_2,r_3,...,r_n)=Ψ(r_1,r_2,r_3,...,r_n,t_{given}[/itex])

    If we knew [itex]f(r_1,r_2,r_3,...,r_n)[/itex] then it were possible to solve QM N-body problem or I also had to use condition that wave function has to be continuous function?
     
  2. jcsd
  3. Jun 30, 2015 #2
    Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
     
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