testing

1 files changed, 59 insertions, 0 deletions

diff --git a/hw8/RadialBoundStates.jl b/hw8/RadialBoundStates.jl
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+++ b/hw8/RadialBoundStates.jl
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+#!/usr/bin/env julia
+
+"""Find eigenstates and eigenenergies of central potential problems"""
+
+using LinearAlgebra
+using Plots
+
+N = 5000  # number of lattice points
+L = 20.0 # r runs from 0 to L
+dr = L / N
+
+D = zeros(N, N) # discrete radial 2nd derivative operator
+V = zeros(N, N) # potential
+
+for i in 1:N
+	D[i, i] = -2.0
+end
+
+for i in 1:N-1
+	D[i, i+1] = 1.0
+	D[i+1, i] = 1.0
+end
+
+#println("\nLattice Laplacian operator")
+#println(D)
+
+function potential(r, ℓ = 0)
+	""" The potential energy"""
+	#return 0.5 * ell * (ℓ+1.0) * pow(r, -2.0) # V=0: Free particle in spherical coordinates	
+
+	return -1.0 / r + 0.5 * ℓ * (ℓ + 1.0) * r^(-2.0) # Hydrogen atom
+
+	#return -r^(-1.1) + 0.5 * ℓ * (ℓ+1.0) * r^(-2.0) # modified Coulomb potential
+end
+
+for i in 1:N
+	r = (i + 0.5) * dr # radial coordinates of lattice points
+	V[i, i] = potential(r, 0)
+end
+
+H = -0.5 * dr^(-2.0) * D + V # Hamiltonian.  Here m = hbar = 1
+
+#println("\nMatrix elements of Hamiltonian = ")
+#println(H)
+
+e, v = eigen(H) # diagonalize Hamiltonian
+
+println("\nGround state energy = ", e[1])
+println("\n1st excited state energy = ", e[2])
+println("\n2nd excited state energy = ", e[3])
+println("\n3rd excited state energy = ", e[4])
+println("\n4th excited state energy = ", e[5])
+
+
+plot(potential)
+
+
+plot(v[:, 1])
+#plot(v[:,2])