val xs = (-3.0 to 3.0 by 0.2).toVector
val ys = (-3.0 to 3.0 by 0.2).toVector
// 2-dimensional quantum harmonic oscillator energy levels
def gaussian2D(x: Double, y: Double): Double = Math.exp(-x*x - y*y)
val z00 = xs.map { x => ys.map { y => gaussian2D(x, y) } }
val z01 = xs.map { x => ys.map { y => y*gaussian2D(x, y) } }
val z11 = xs.map { x => ys.map { y => x*y*gaussian2D(x, y) } }
val z20 = xs.map { x => ys.map { y => (1-2*x*x)*gaussian2D(x, y) } }
val options = SurfaceOptions().noScale
val figure = GridFigure(2, 2) // four plots split over two rows
.title("Eigenfunctions of the 2D quantum harmonic oscillator")
.plot(0, 0) { // top left
ThreeDPlot()
.withSurface(xs, ys, z00, options)
.zAxisOptions(AxisOptions().title("psi_00"))
}
.plot(0, 1) { // top right
ThreeDPlot()
.withSurface(xs, ys, z01, options)
.zAxisOptions(AxisOptions().title("psi_01"))
}
.plot(1, 0) { // bottom left
ThreeDPlot()
.withSurface(xs, ys, z11, options)
.zAxisOptions(AxisOptions().title("psi_11"))
}
.plot(1, 1) { // bottom right
ThreeDPlot()
.withSurface(xs, ys, z20, options)
.zAxisOptions(AxisOptions().title("psi_20"))
}
draw(figure, "qho-eigenfunctions")
