Add test for infinite potential well

7 files changed, 86 insertions, 29 deletions

diff --git a/.gitignore b/.gitignore
index 251d000..8b15847 100644
--- a/.gitignore
+++ b/.gitignore
@@ -2,3 +2,4 @@ docs/_build
 .idea/
 schroedinger/__pycache__
 notes.org
+**/__pycache__
diff --git a/schroedinger/__init__.py b/schroedinger/__init__.py
index 1de4510..e952971 100644
--- a/schroedinger/__init__.py
+++ b/schroedinger/__init__.py
@@ -1 +1 @@
-from .schroedinger import Config
+from .schroedinger import *
diff --git a/schroedinger/schrodinger_solve.py b/schroedinger/schrodinger_solve.py
index 618d4ce..8f9f515 100644
--- a/schroedinger/schrodinger_solve.py
+++ b/schroedinger/schrodinger_solve.py
@@ -1,35 +1,11 @@
 import argparse
 
 import numpy as np
-from scipy.linalg import eigh_tridiagonal
 
-from schroedinger import Config, potential_interp
-
-def build_potential(config: Config):
-    start, end, steps = config.interval
-    potential = np.zeros((steps, 2))
-    potential[:, 0] = np.linspace(start, end, steps)
-    delta = np.abs(potential[1, 0] - potential[0, 0])
-    interp = potential_interp(config.interpolation, config.points)
-    potential[:, 1] = interp(potential[:, 0])
-    return potential, delta
-
-
-def solve_schroedinger(mass, potential, delta, eig_interval=None):
-    '''
-    returns eigen values and wave functions specified by eig_interval
-    '''
-    n = potential.shape[0]
-    a = 1 / mass / delta**2
-    w, v = eigh_tridiagonal(a + potential,
-                            -a * np.ones(n - 1, dtype=np.float_) / 2.0,
-                            select='i', select_range=eig_interval)
-    # Normalize eigenfunctions
-    for i in range(w.shape[0]):
-        v[:, i] /= np.sqrt(delta * np.sum(np.abs(v[:, i])**2))
-
-    return w, v
+from schroedinger import (
+    Config, potential_interp, build_potential, solve_schroedinger
 
+)
 
 def save_wavefuncs(filename, x, v):
     wavefuncs = np.zeros((x.shape[0], v.shape[1] + 1))
diff --git a/schroedinger/schroedinger.py b/schroedinger/schroedinger.py
index 10d994e..3ed2c3f 100644
--- a/schroedinger/schroedinger.py
+++ b/schroedinger/schroedinger.py
@@ -4,6 +4,7 @@ import numpy as np
 from numpy.polynomial import Polynomial
 from numpy.typing import NDArray
 from scipy.interpolate import CubicSpline
+from scipy.linalg import eigh_tridiagonal
 
 class Config:
     def __init__(self, path):
@@ -29,7 +30,7 @@ class Config:
                 self.mass = float(next_parameter(fd))
                 start, end, steps = next_parameter(fd).split()
                 self.interval = [float(start), float(end), int(steps)]
-                self.eig_interval = [int(attr) for attr in next_parameter(fd).split()]
+                self.eig_interval = [int(attr) - 1 for attr in next_parameter(fd).split()]
                 self.interpolation = next_parameter(fd)
 
                 npoints = int(next_parameter(fd))
@@ -57,3 +58,29 @@ def potential_interp(interpolation, points):
         return cs
 
     raise ValueError()
+
+
+def build_potential(config: Config):
+    start, end, steps = config.interval
+    potential = np.zeros((steps, 2))
+    potential[:, 0] = np.linspace(start, end, steps)
+    delta = np.abs(potential[1, 0] - potential[0, 0])
+    interp = potential_interp(config.interpolation, config.points)
+    potential[:, 1] = interp(potential[:, 0])
+    return potential, delta
+
+
+def solve_schroedinger(mass, potential, delta, eig_interval=None):
+    '''
+    returns eigen values and wave functions specified by eig_interval
+    '''
+    n = potential.shape[0]
+    a = 1 / mass / delta**2
+    w, v = eigh_tridiagonal(a + potential,
+                            -a * np.ones(n - 1, dtype=np.float_) / 2.0,
+                            select='i', select_range=eig_interval)
+    # Normalize eigenfunctions
+    for i in range(w.shape[0]):
+        v[:, i] /= np.sqrt(delta * np.sum(np.abs(v[:, i])**2))
+
+    return w, v
diff --git a/test/__init__.py b/test/__init__.py
new file mode 100644
index 0000000..8b13789
--- /dev/null
+++ b/test/__init__.py
@@ -0,0 +1 @@
+
diff --git a/test/infinite.inp b/test/infinite.inp
new file mode 100644
index 0000000..a61ffbe
--- /dev/null
+++ b/test/infinite.inp
@@ -0,0 +1,7 @@
+2.0             # mass
+-2.0 2.0 1999   # xMin xMax nPoint
+1 5             # first and last eigenvalue to print
+linear          # interpolation type
+2               # nr. of interpolation points and xy declarations
+-2.0 0.0
+2.0 0.0
diff --git a/test/test_infinite.py b/test/test_infinite.py
new file mode 100644
index 0000000..aa85ae5
--- /dev/null
+++ b/test/test_infinite.py
@@ -0,0 +1,45 @@
+import pytest
+import numpy as np
+
+import matplotlib.pyplot as plt
+
+from schroedinger import (
+    Config, potential_interp, build_potential, solve_schroedinger
+)
+
+
+def psi(x, n, a):
+    n += 1 # Index starting from 0
+    x = -x + a / 2 # Reflect x and move to the left
+    return np.sqrt(2 / a) * np.sin(n * np.pi * x / a)
+
+
+def energy(n, a, m):
+    return (n + 1)**2 * np.pi**2 / m / a**2 / 2.0
+
+
+def test_infinite():
+    conf = Config('test/infinite.inp')
+    potential, delta = build_potential(conf)
+
+    e, v = solve_schroedinger(conf.mass, potential[:, 1], delta, conf.eig_interval)
+    # Account for -v also being an eigenvector if v is one
+    v = np.abs(v)
+
+    a = np.abs(conf.points[1][0] - conf.points[0][0])
+    e_theory = np.zeros(e.shape)
+    v_theory = np.zeros(v.shape)
+
+
+    for n in range(e.shape[0]):
+        e_theory[n] = energy(n, a, conf.mass)
+        v_theory[:, n] = np.abs(psi(potential[:, 0], n, a))
+
+    # for n in range(e.shape[0]):
+    #     plt.plot(potential[:, 0], np.abs(v[:, n]), label='Num{}'.format(n))
+    #     plt.plot(potential[:, 0], np.abs(v_theory[:, n]), ls='--', label='Theory{}'.format(n))
+    # plt.legend()
+    # plt.savefig('test.pdf')
+
+    assert (np.allclose(e, e_theory, rtol=1e-2, atol=1e-2)
+            and np.allclose(v, v_theory, rtol=1e-2, atol=1e-2))