From 4df4fb0c6119e039f5e7994a10773c2395431b12 Mon Sep 17 00:00:00 2001
From: orosmatthew <orosmatthew@pm.me>
Date: Tue, 23 Apr 2024 12:29:24 -0400
Subject: [PATCH] Update numerov

---
 numerov.py => numerov-1.py | 10 --------
 numerov-2.py               | 52 ++++++++++++++++++++++++++++++++++++++
 2 files changed, 52 insertions(+), 10 deletions(-)
 rename numerov.py => numerov-1.py (85%)
 create mode 100644 numerov-2.py

diff --git a/numerov.py b/numerov-1.py
similarity index 85%
rename from numerov.py
rename to numerov-1.py
index 1edc43a..7195162 100644
--- a/numerov.py
+++ b/numerov-1.py
@@ -1,13 +1,3 @@
-"""
---- Title:      Schrodinger Equation in Harmonic Potential
---- Author:     Matt Evans (mtdevans.com)
---- Copyright:  Do what you want with it.
-
-This program basically just draws the functions for a
-given value of epsilon. Epsilon should be an integer n+1/2
-for good solutions.
-"""
-
 import pylab as lab
 
 iterations = 60000  # iterations for approximation
diff --git a/numerov-2.py b/numerov-2.py
new file mode 100644
index 0000000..7195162
--- /dev/null
+++ b/numerov-2.py
@@ -0,0 +1,52 @@
+import pylab as lab
+
+iterations = 60000  # iterations for approximation
+
+step = 0.0001  # step size for x
+step_sqrd = pow(step, 2)  # square of step size
+
+epsilon = 2.5  # energy level, should be integer n+1/2 for good solutions
+
+psi = 0.0  # initial value of wave function
+potential = 0.0  # initial value of the potential energy function
+pos = -1 * (iterations - 2) * step  # initial value of the position
+
+potential_past_2 = epsilon + pos - 2 * step  # k_0, potential energy at two steps before current
+potential_past_1 = epsilon + pos - step  # k_1, potential energy at one step before current
+amplitude = 0.1  # initial amplitude of wave function
+psi_past_2 = 0  # y_0, wave function at two steps before current
+psi_past_1 = amplitude  # y_1, wave function at one step before current
+
+x_out = []  # list to store x values for plotting
+y_out = []  # list to store y values for plotting
+
+count = -1 * iterations + 2  # counter for the loop
+
+# Numerov integration loop
+while count < iterations - 2:
+    count += 1
+    pos += step
+    potential = 2 * epsilon - pow(pos, 2)  # potential energy function
+    b = step_sqrd / 12  # constant used for Numerov
+    # Numerov method to calculate psi at current step
+    psi = ((2 * (1 - 5 * b * potential_past_1) * psi_past_1 - (1 + b * potential_past_2) * psi_past_2)
+           / (1 + b * potential))
+
+    # Save for plotting
+    x_out.append(pos)
+    y_out.append(psi)
+
+    # Shift for next iteration
+    psi_past_2 = psi_past_1
+    psi_past_1 = psi
+    potential_past_2 = potential_past_1
+    potential_past_1 = potential
+
+# Plot
+lab.figure(1)
+lab.plot(x_out, y_out, label=f'epsilon = {epsilon}')
+lab.xlabel("x")
+lab.ylabel("y")
+lab.title("Schrodinger Eqn in Harmonic Potential")
+lab.legend(loc=1)
+lab.show()