I am trying to solve a Schrödinger equation for a particle hitting a step potential using NDSolve
in Mathematica. Here is my code:
mu = 6.;
m = mu;
R = 5.;
Vs2 = 4./(2*m*R^2);
Vs = -10./(2*m*R^2) + Vs2;
Energy = 0.001
VCC[r_] = Vs*UnitStep[R - r] + Vs2*UnitStep[r - R];
L = 0;
system = {RC''[r] +
2/r*RC'[r] + (-L*(L + 1)/r^2 - 2*mu*(VCC[r] - Energy))*RC[r] ==
0, RC[0.001] == 1.0, RC'[0.001] == 0.0 };
syssol = NDSolve[system, {RC[r]}, { r, 0.001, 1000.}, MaxSteps -> 10000000];
Plot[Evaluate[{RC[r]} /. syssol], {r, 0.001, 200.0}, PlotRange -> {-1.1, 1.1}]
There should be decaying wave when particle hits the potential step, but NDSolve
gives an increasing result. I am sure there is some trick to fix this, so I am waiting for you help.
m
? Also take a look at this (it's a bit different case but you can see how everything is set up): demonstrations.wolfram.com/ScatteringOverPotentialStep $\endgroup$ – Vitaliy Kaurov Mar 25 '12 at 18:39m
here (this is to make it simpler for someone to cut and paste this code directly) $\endgroup$ – acl Mar 25 '12 at 18:43