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psi_dt = function (psi, expV, expK, expABC) {
psi = cmultiply(psi, expV) // step 1
psi = nj.fft(psi) // step 2 - FT
psi = cmultiply(psi, expK) // step 2
psi = nj.ifft(psi) // step 2 - Inverse FT
psi = cmultiply(psi, expV) // step 3
psi = cmultiply(psi, expABC) // Absorbing boundary condition
return psi
}
x = nj.arange(numx).multiply(dx).subtract(xmax).reshape(numx,1)
k = fftfreq(x)
expK = cexp(k.pow(2).multiply(-dt))
V = x.pow(2)
expV = cexp(V.multiply(-dt/2))
expABC = {
let absorb = nj.tanh(x.subtract(xmax).divide(w)).add(2).subtract(nj.tanh(x.add(xmax).divide(w))).multiply(-lambda*dt)
let expABC = nj.exp(absorb)
expABC = nj.concatenate(expABC, nj.zeros([numx,1]) ) // need to add 2nd column of zeros for the zero imaginary part
return expABC
}
psi0 = nj.concatenate(nj.exp(x.subtract(1).pow(2).multiply(-1)), nj.zeros([numx,1]) ).multiply(Math.pow(2 / Math.PI, 0.25))
psi0_squared = cnorm2(psi0).multiply(10) // x10 to make it more visible on the plot
mutable psi=psi0 // This sets the initial condition for the simulation of psi
// Note, for more info on "mutable" see https://observablehq.com/@mbostock/mutable-values
{
if(simulate===true) { // Only simulate when simulation checkbox has been checked
mutable psi = psi_dt(psi, expV, expK, expABC) // This runs the simulation indefinitely
}
return "Indefinite simulation loop"
}
psi_squared = cnorm2(psi).multiply(10) // x10 to make it more visible on the plot
graph.update([x,psi_squared,V])
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