Quantum 2D particle in an electromagnetic field

This is a live simulation of a quantum particle in an electromagnetic field. In order to keep the controls relatively simple, right now it only supports uniform, constant fields. It utilizes an interesting numerical algorithm that is both explicit (don't need to solve algebraic equations like Crank-Nicholson), and unitary (probability is conserved and the simulation is unconditionally stable). For more information, see the project on GitHub. Below is a description of the parameters (note that we are using units where c=hbar=m=q=1):

• Bz: the magnetic field strength in the direction perpendicular to the screen; positive values denote field oriented outward, negative values reverse direction of the field.
• |E⃗|, θ: the magnitude and direction of the electric field in the plane of the screen, respectively. θ=0 points to the right and increases counter-clockwise.
• (x₀, y₀): the initial position of the wave packet on the lattice.
• σ: the initial width of the wave packet.
• |p⃗₀|, θ₀: the initial momentum/direction of the wave packet. p is specified in multiples of k=2π/L
• N: the number of grid points along each edge of the simulation. (L is the actual physical length; i.e. (N-1)*dx)
• dx: the physical spacing between grid points.
• dt: the amount of time between each time step of the simulation.

Any changes to the parameters will not take effect until you click the "Reset" button.