Numerical solution of the 3D Schrodinger equation for the hydrogen atom

Simulation of the time evolution of the wave equation for an electron in a hydrogen atom:

ih∂ρ/∂t=-h*h/(2m) Δρ- kρ/r

Where i is the imaginary number, ρ is the dependent variable (the square of which gives the probability density), h a constant, m the particle mass, r the radial coordinate, t time and k a constant depending on the charge of the particle. The initial value of ρ at t = 0 is 0.5 + 0.5i, i.e: ρ(r,θ,ϕ,0) = 0.5 + 0.5i. The graphs are the solutions as a function of the radial coordinate. The blue line gives the real part of the solution and the orange line the imaginary part.

The code can be found at: