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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.

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# Nonlinear equation and state superposition

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