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Nonlinear equation and state superposition

  1. Dec 4, 2015 #1
    Hi,

    In quantum physics, solution of Shrodinger equation live in a Hilbert space which is a vector space. The state superposition is obtained by mixing solution of the équation which is LINEAR so a linear combination of solution is a solution.

    Now i have a non-linear equation of a scalar field named Q. So a linear combination of solution of Q is not a solution. To obtain a state superposition, i define a probability density P over the space of all scalar field which is a functionnal space. Is it a good way ? did you know similar aproach ?

    Because, now at the oposite of Shrodinger equation, the time evolution is a modification of density P over time. I have strong difficulties to write the equation which control P over time because it need to derivate a scalar field defined over a function space.

    Thanks for your answer.
     
  2. jcsd
  3. Dec 9, 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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