# Non-Linear Schroedinguer equation

1. Jun 30, 2006

### eljose

Let be the NOn-linear Schroedinguer equation:

$$i\hbar \frac{\partial \psi}{\partial t}=-\hbar^{2}(2m)^{-1} \nabla ^{2} \psi + |\psi|^{3}$$

for example..the question is..how the hell do you solve it for certain boundary conditions that the Wavefunction must satisfy if you can,t apply superposition principle?...How do you express the probability of finding a particle in state a with energy E_a?..

2. Jun 30, 2006

### Careful

(c) One should not interpret the $$\psi$$ wave associated to the NLSE as a probability density - there is however a clever'' way to get to the standard probablity interpretation; see combining relativity and quantum mechanics : Schroedingers interpretation'' A.O. Barut 1987.