The extra parameter, $\alpha$ isn't a physical thing, but we'll need it to make sure that we don't have a 1/0 value for the potential anywhere.
// This returns an empty wavefunction of length n. function wavefunction(n){ var psi = []; for(var i = 0; i < n; i++){ psi[i]=[]; for(var j = 0; j < n; j++){ psi[i][j] = {real: 0, imag: 0} } } return psi; // for example [{real:0, imag:0}, {real:0, imag:0}, ...] } // This takes the starting wavefunction, and returns the wavefunction a short time later. function timestep(psi) { // This is how many units of time we're going to try to step forward. var dt = 0.02; psi = timestepV(psi, dt); psi = timestepT(psi, dt); return psi; } function timestepV(psi, dt) { var n = psi.length; for(var i = 0; i < n; i++) { for(var j = 0; j < n; j++){ // This is the x that is in the equation above. var x = (i-n/2) var y = (j-n/2) // This is the potential at this point. var V = 1.0 / Math.sqrt(x*x + y*y + .01); var theta = dt * V; var c = Math.cos(theta); var s = Math.sin(theta); var re = psi[i][j].real * c - psi[i][j].imag * s; var im = psi[i][j].imag * c + psi[i][j].real * s; psi[i][j].real = re; psi[i][j].imag = im; } } return psi; } function timestepT(psi, dt){ psi = FFT.fft2d(psi); var n = psi.length; for(var i = 0; i < n; i++) { for(var j=0;j < n; j++) { var k = 2 * 3.1415927 * Math.min(i, n-i) / n; var l = 2 * 3.1415927 * Math.min(j, n-j) / n; var theta = (k * k + l*l) * dt; var c = Math.cos(-theta); var s = Math.sin(-theta); var re = psi[i][j].real * c - psi[i][j].imag * s; var im = psi[i][j].imag * c + psi[i][j].real * s; psi[i][j].real = re; psi[i][j].imag = im; } } return FFT.fft2d(psi); } // This returns the initial state of the simulation. function init(){ var n = 64; var psi = wavefunction(n); for(var i = 0; i < n; i++){ for(var j = 0; j < n; j++){ psi[i][j].real = Math.exp(-((i-20)*(i-20) + (j-20)*(j-20))/(5*5))*4; psi[i][j].imag = 0; } } return psi; }
The double slit and observersA look at the double slit experiment. The first half is meant to be a clear explanation, using simulations. The second half discusses some of the philosophy / interpretations of quantum mecahnics. |
BodyWorks: Kinematics ToolA page with a javascript application where you can set body positions, calculate joint angles and animate human motion. |
BodyWorks: Neuromuscular Activity / Muscle EMGAn interactive simulation showing how nerves travel to and down muscles, and how this gets picked up by EMG sensors. |
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