A Nonlinear Schrodinger equation and linearity of Q.M.

[Buddha_the_Scientist]

Hello all,
you may already know that Q.M. is a linear theory however there is something called nonlinear Sch. eq. for example Gross-Pitaevskii equation. How can such a thing exist considering that Q.M. is a strictly linear theory.
Cheers.

 

[A. Neumaier]

It is an approximation obtainable from quantum field theory. This is nothing special; many PDEs arise in this way. For example, the Navier-Stokes equations are also approximations obtainable from QFT.

 

[Buddha_the_Scientist]

Thank you Prof. Neumaier.
So it is an approximation for ease of calculations. Because I feel like if linearity is violated the theory shouldn't be reversible which might have serious consequences, also it might be possible to clone quantum states and faster than light signalling must be possible. But you are saying if one needs an exact calculation everything would be eventually linear, right?

 

[A. Neumaier]

if one needs an exact calculation everything would be eventually linear, right?

Yes, the Schroedinger equation still holds exactly in quantum field theory.