Science, technology, education
x = nj.arange(numx).multiply(dx).subtract(xmax).reshape(numx,1)
k = fftfreq(x)
V = {
let outside_right = nj.zeros(Math.round((numx-1)/2)) // this should make the potential free region start at 0
let barrier = nj.ones(Math.round(barrier_width/dx)).multiply(barrier_height)
let well = nj.zeros(Math.round(well_width/dx))
let outside_left = nj.ones(numx - Math.round(well_width/dx) - Math.round(barrier_width/dx) - Math.round((numx-1)/2) ).multiply(barrier_height)
let V = nj.concatenate(outside_left,well,barrier,outside_right)
return V.reshape(numx,1)
}
well_start = numx - Math.round(well_width/dx) - Math.round(barrier_width/dx) - Math.round((numx-1)/2)
well_end = well_start + Math.round(well_width/dx)
V_plot = V.divide(barrier_height)
expK = cexp(k.pow(2).multiply(-dt*(2*Math.PI)**2.0))
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
}
x0 = - barrier_width - well_width/2
psi0 = {
let sigma2 = 2
let norm_constant = Math.pow(2 / (Math.PI * sigma2), 0.25);
let psi0 = nj.concatenate(nj.exp(x.subtract(x0).pow(2).multiply(-1).divide(sigma2)), nj.zeros([numx,1]) )
psi0 = cmultiply(psi0,cexp(x.multiply(p0)))
return psi0.multiply(norm_constant);
}
psi0_squared = cnorm2(psi0)
P_well0 = psi0_squared.slice([well_start,well_end]).sum()*dx
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
mutable psi_plot = psi0
mutable P_well = nj.array([P_well0]) // this creates an array to store the evolving values of P_well
mutable time = nj.array([0]) // this creates an array to store the evolving time for plotting along with P_well
mutable i = 0 // this keeps track of the number of the elapsed timesteps
reset = function(){
mutable psi = psi0;
mutable psi_plot = psi0;
mutable time = nj.array([0])
mutable P_well = nj.array([P_well0])
mutable i =0
}
{
if(simulate===true) { // Only simulate when simulation checkbox has been checked
mutable psi = psi_dt(psi, expV, expK, expABC)
// Update the timestep
mutable i+=1
// Only update the psi_plot for plotting every n time-steps
if(i%n==0) {
mutable psi_plot = psi // Note this line will trigger psi_squared for the plots and also for the next step below
// Add new data to the P_well and time arrays by concatenating old array with new value
mutable P_well = nj.concatenate(mutable P_well,nj.array([psi_squared.slice([well_start,well_end]).sum()*dx]))
mutable time = nj.concatenate(mutable time, nj.array([i*dt]))
}
}
return "Indefinite simulation loop"
}
psi_squared = cnorm2(psi_plot)
graph.update([x,psi_squared,V_plot]) // Update the simulation plot when new values of psi_plot are available
graph_P_well.update([nj.stack([time, P_well], -1)]) // Update the simulation plot when new values of P_well are available
Purpose-built for displays of data
Observable is your go-to platform for exploring data and creating expressive data visualizations. Use reactive JavaScript notebooks for prototyping and a collaborative canvas for visual data exploration and dashboard creation.
