From e650ed1e1e908e51c78c1b047bec0da7c4fea366 Mon Sep 17 00:00:00 2001
From: sotech117 <michael_foiani@brown.edu>
Date: Sat, 27 Apr 2024 04:25:23 -0400
Subject: testing

---
 hw8/BoundStates.jl | 73 ++++++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 73 insertions(+)
 create mode 100644 hw8/BoundStates.jl

(limited to 'hw8/BoundStates.jl')

diff --git a/hw8/BoundStates.jl b/hw8/BoundStates.jl
new file mode 100644
index 0000000..22e608c
--- /dev/null
+++ b/hw8/BoundStates.jl
@@ -0,0 +1,73 @@
+#!/usr/bin/env julia
+
+"""Find eigenstates and eigenenergies of 1-D quantum problems"""
+
+using LinearAlgebra
+using Plots
+
+N = 1000  # number of lattice points
+L = 20.0 # x runs from -L/2 to L/2
+dx = L / N
+
+D = zeros(N, N) # discrete laplacian 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(x)
+	""" The potential energy"""
+	#return 0.0 # particle in a box
+	#return 0.5 * x^2 # SHO with the spring constant k = 1
+	#return -6.0 * x^2 + 8.0 * x^6 # potential with zero ground state energy
+	#return 0.1 * x^4 - 2.0 * x^2 + 0.0 * x # double-well potential
+	return 8 * x^6 - 8 * x^4 - 4 * x^2 + 1 # another double-well potential
+end
+
+for i in 1:N
+	x = (i + 0.5) * dx - 0.5 * L # coordinates of lattice points
+	V[i, i] = potential(x)
+end
+
+H = -0.5 * dx^(-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])
+
+
+gs(x) = exp(-0.5 * x^2) # Gaussian that is exact ground state of SHO
+
+
+plot(potential)
+
+
+plot(v[:, 1])
+#plot(v[:,2])
+#plot(gs)
+
+#=
+eList = zeros(0)
+for i in 1:20
+	push!(eList, e[i])
+end
+
+
+bar(eList, orientation = :horizontal)
+=#
-- 
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