Specifying the norm of complex function

[Elliotepsteino]

I aim to solve the nonlinear Schrödinger equation, see: https://en.wikipedia.org/wiki/Nonlinear_Schr%C3%B6dinger_equation. To do this with py-pde I need to specify the norm of a complex valued function, my guess is that I should use ψ ** 2, and specify the full equation as PDE({"ψ": f"I * 0.5* laplace(ψ)+I*(ψ *(ψ**2))"}. However, the results don't align with what I expect to see. Any tips on how to do this?

[david-zwicker]

The expression ψ**2 is not calculating the squared norm, but it is equivalent to ψ*ψ. To calculate the squared norm you could either use abs(ψ)**2, which returns a real number, or ψ * conjugate(ψ), which returns a complex number (with vanishing imaginary part). Both versions should work equally well, although I have not tested this in detail.

[Elliotepsteino]

Hi David, ψ * conjugate(ψ) works! However, abs(ψ)**2 gives an error for me.

[david-zwicker]

I guess it's good that one approach worked for you, but I'm puzzled that abs(ψ)**2 did not. Could you copy the error message here?