testing

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diff --git a/hw8/10-3.jl b/hw8/10-3.jl
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+#!/usr/bin/env julia
+
+"""Find eigenstates and eigenenergies of 1-D quantum problems"""
+
+using LinearAlgebra
+using Plots
+
+#println("\nLattice Laplacian operator")
+#println(D)
+
+function potential(x, n)
+	""" 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
+	return abs(x)^n
+end
+
+#println("\nMatrix elements of Hamiltonian = ")
+#println(H)
+
+
+function map_n_to_energies(n)
+	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
+
+
+	for i in 1:N
+		x = (i + 0.5) * dx - 0.5 * L # coordinates of lattice points
+		V[i, i] = potential(x, n)
+	end
+
+	H = -0.5 * dx^(-2.0) * D + V # Hamiltonian.  Here m = hbar = 1
+
+
+	e, v = eigen(H) # diagonalize Hamiltonian
+
+	println("\n n = ", n)
+	println("Ground state energy = ", e[1])
+	println("1st excited state energy = ", e[2])
+	println("2nd excited state energy = ", e[3])
+	println("3rd excited state energy = ", e[4])
+	println("4th excited state energy = ", e[5], "\n")
+
+	return e
+end
+
+n_max = 18
+n_to_e = [map_n_to_energies(n) for n in 1:n_max]
+
+# plot e[0] for all N
+eList = zeros(0)
+for i in 1:n_max
+	push!(eList, n_to_e[i][1])
+end
+
+plot(eList)
+
+# 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)
+=#