finish hw8, the last hw

12 files changed, 78 insertions, 1 deletions

diff --git a/.DS_Store b/.DS_Store
index 2b5a296..1d1ed19 100644
--- a/.DS_Store
+++ b/.DS_Store
diff --git a/hw8/10-17-new.jl b/hw8/10-17-new.jl
new file mode 100644
index 0000000..1353618
--- /dev/null
+++ b/hw8/10-17-new.jl
@@ -0,0 +1,75 @@
+using Plots
+using LinearAlgebra
+
+m = 1
+hbar = 1
+xmin = -6.5
+xmax = 6.5
+N = 2000
+x = collect(range(xmin, stop = xmax, length = N + 1)) # one extra, want 1000 spaces
+dx = x[2] - x[1]
+println("dx = ", dx)
+p = 100.0
+V0 = 2 * p^2 / (2.0 * m)
+sig = 0.25
+x0 = 2.0 # a bit away to not interfere with the walls
+barrier_width = 0.025
+
+# setup the potential barrier
+V = 0 .* x
+# println("V = ", length(V))
+for i in 1:length(V)
+	if x[i] > 0 && x[i] < barrier_width
+		V[i] = V0
+	end
+end
+plot(x, V, xlabel = "x", ylabel = "V(x)", title = "Potential V(x)", legend = :none)
+
+# make the initial wavefunction
+psi0 = exp.(-((x[2:end-1] .+ x0) .^ 2) / (2 * sig^2)) .* exp.(1.0im * p * x[2:end-1])
+C = sum(abs2.(psi0) .* dx)
+psi0 = psi0 / sqrt(C)
+plot(x[2:end-1], abs.(psi0), xlabel = "x", ylabel = "Re(psi)", title = "Initial wavefunction", legend = :none)
+
+# make the Hamiltonian
+A = (hbar^2 / (2 * m * dx^2))
+# main diagonal
+d = A * ones(N - 1) + V[2:end-1] # add potential
+# upper and lower diagonals
+dl = (A / -2.0) * ones(N - 2)
+du = (A / -2.0) * ones(N - 2)
+H = Tridiagonal(dl, d, du)
+
+# diagonalize matrix
+E, psi = eigen(H)
+psi1 = psi[:, 1]
+
+# normalize
+A = sum(abs2.(psi1) .* dx)
+psi = psi ./ sqrt(A)
+println("A = ", A)
+
+c = zeros(ComplexF64, length(psi[:, 1]))
+for i in 1:length(c)
+	c[i] = sum(conj.(psi[:, i]) .* psi0 .* dx)
+end
+
+dt = 0.0001
+
+anim = @animate for t in 0:dt:0.25
+	tmp = zeros(ComplexF64, length(psi[:, 1]))
+	for i in 1:length(c)
+		tmp = tmp .+ c[i] .* exp.(-1.0im * E[i] * t / hbar) .* psi[:, i]
+	end
+	rounded_p = round(p, digits = 3)
+	rounded_pot = round(V0, digits = 3)
+	plot(x[2:end-1], abs.(tmp), xlabel = "x", ylabel = "abs(Ψ)", title = "Propagating Wavepacket (k_0 = $p, V0 = $rounded_pot)", label = "psi @ t = $t", ylims = (-2, 2), lw = 2)
+	# plot the real
+	plot!(x[2:end-1], real(tmp), xlabel = "x", label = "real")
+	# plot the imaginary
+	plot!(x[2:end-1], imag(tmp), xlabel = "x", label = "imag")
+	plot!([endpoint_1, endpoint_1], [0, 2], label = "", line = :dash, color = :red)
+	plot!([endpoint_2, endpoint_2], [0, 2], label = "barrier (width = $barrier_width)", line = :dash, color = :red)
+end
+
+mp4(anim, "hw8/10-17-tunnelling-$barrier_width-$p.mp4", fps = 30)
\ No newline at end of file
diff --git a/hw8/10-17-tunnelling-0.025-200.0.mp4 b/hw8/10-17-tunnelling-0.025-200.0.mp4
new file mode 100644
index 0000000..49b9c9f
--- /dev/null
+++ b/hw8/10-17-tunnelling-0.025-200.0.mp4
diff --git a/hw8/10-17-tunnelling-0.025-40.0.mp4 b/hw8/10-17-tunnelling-0.025-40.0.mp4
new file mode 100644
index 0000000..9b80be7
--- /dev/null
+++ b/hw8/10-17-tunnelling-0.025-40.0.mp4
diff --git a/hw8/10-17-tunnelling-0.025.mp4 b/hw8/10-17-tunnelling-0.025.mp4
new file mode 100644
index 0000000..49b9c9f
--- /dev/null
+++ b/hw8/10-17-tunnelling-0.025.mp4
diff --git a/hw8/10-17-tunnelling-0.05-200.0.mp4 b/hw8/10-17-tunnelling-0.05-200.0.mp4
new file mode 100644
index 0000000..25ebb7d
--- /dev/null
+++ b/hw8/10-17-tunnelling-0.05-200.0.mp4
diff --git a/hw8/10-17-tunnelling-0.05-40.0.mp4 b/hw8/10-17-tunnelling-0.05-40.0.mp4
new file mode 100644
index 0000000..9b3124f
--- /dev/null
+++ b/hw8/10-17-tunnelling-0.05-40.0.mp4
diff --git a/hw8/10-17-tunnelling-0.05.mp4 b/hw8/10-17-tunnelling-0.05.mp4
new file mode 100644
index 0000000..b247200
--- /dev/null
+++ b/hw8/10-17-tunnelling-0.05.mp4
diff --git a/hw8/10-17-tunnelling-0.1.mp4 b/hw8/10-17-tunnelling-0.1.mp4
new file mode 100644
index 0000000..f2ba8b9
--- /dev/null
+++ b/hw8/10-17-tunnelling-0.1.mp4
diff --git a/hw8/10-17.jl b/hw8/10-17.jl
index d1d18b7..6690d1f 100644
--- a/hw8/10-17.jl
+++ b/hw8/10-17.jl
@@ -16,7 +16,9 @@ function H(psi, dx, k = 0, width = 0.1) # action of Hamiltonian on wavefunction
 	for i in 1:length(psi)
 		x = i * dx
 		if x >= 30.0 && x <= 30.0 + width
-			Hpsi[i] = 2 * k^2 * psi[i]
+			Hpsi[i] += 2 * k^2
+			# else
+			# 	Hpsi[i] += -0.01
 		end
 	end
 
diff --git a/hw8/10-17.png b/hw8/10-17.png
new file mode 100644
index 0000000..9f76c42
--- /dev/null
+++ b/hw8/10-17.png
diff --git a/hw8/wavefunction.png b/hw8/wavefunction.png
new file mode 100644
index 0000000..5ad2d78
--- /dev/null
+++ b/hw8/wavefunction.png