#Quantum.js Javascript simulator for particles in a box.

#Getting Started Currently, functionality is non-existent. Run ./run-tests.py to execute unit-tests. Eventually, you should run some sort of standard setup script.

Still in implementation phase.

The simulator works by choosing an orthogonal basis of states, and then computing the individual kinetic and potential energy contributions, weighted by the coefficient of that state to the total Hamiltonian time step.

The basis that will be chosen is intented to be position based, however, I'll have to figure out how to choose an appropriate basis function to ensure each state has finite kinetic energy, and are all orthogonal to each other.

Okay, let's talk about the idea here again.

In quantum mechanics, we have a wave function, and we need to evolve it over time.

The schroedinger equation says:

\partial{Psi}{dt} = ih H\Psi

Where H is the Hamiltonian. The classic Schroedinger equation that we typically think of

\frac{hbar^2}{2 m}\partial2{Psi(x,t)}{dx^2} + V(x,t)\Psi(x,t) = ih \partial{Psi}{dt}

Works on the basis of all L^2 functions of position and time. Again, it's extremely important to talk about what basis you're representing \Psi in. The actual kinetic energy of a basis state that is "mostly" restricted to a given region will change depending on the exact.

One problem with this approach is that our basis functions won't be actually complete. If we assign a finite basis, then projecting an arbitrary wave function onto it will "leak" some of it. Worse the actual amlitude of that leakage may not remain small over time. This is one of the major nice aspects of the energy basis, we're guaranteed that the total amplitude of ignored terms is bounded over time.