What Free Programs Exist for Simulating Multi-Particle Quantum Mechanics?

[dsoodak]

http://www.falstad.com/qm1d/
is a really good way of getting a feel for the dynamics of a single particle in a variety of potential wells.
Does anyone know of an equivalent (hopefully free) program for multi-particle systems?

Dustin Soodak

 

[The_Duck]

Well, the same guy has some QM applets for a single particle in 2D. You could take these and reinterpret the x and y coordinates as the coordinates of two particles each moving in 1D, and the potential V(x, y) as an interaction potential.

 

[dsoodak]

So you can just calculate the total potential energy of the charged particles with each other and the background field and treat it as one particle moving in 2D? I was afraid I would have to keep iterating the wavefunctions and electrical potentials until they both got to stable values...

I am still unclear on exactly what happens to the wavefunctions when you have more than 2 fermions interacting. Exactly 2 is generally explained by saying that they are always 180 degrees (in complex plane) out of phase so cancel out when on top of each other, but this idea doesn't work for 3 objects without some modification.

I was originally going to ask both of these questions in separate threads but then figured it would be easier if I could just look at an existing simulation.

 

[The_Duck]

So you can just calculate the total potential energy of the charged particles with each other and the background field and treat it as one particle moving in 2D?

Yes, the Schrödinger equation looks formally the same in both cases.

I am still unclear on exactly what happens to the wavefunctions when you have more than 2 fermions interacting.

A three-fermion wave function is a complex function of three positions: $\psi(x_1, x_2, x_3)$. It must obey the condition

$\psi(x_1, x_2, x_3) = \psi(x_2, x_3, x_1) = \psi(x_3, x_1, x_2) = -\psi(x_2, x_1, x_3) = -\psi(x_1, x_3, x_2) = -\psi(x_3, x_2, x_1)$

i.e., swapping any two arguments must give an overall minus sign. If you start with a wave function obeying this condition and then evolve it in time according to the Schrödinger equation, it will keep obeying this condition.

 

[dsoodak]

Thanks! That clarified a couple of things I've been trying to work out.