Add problems

.idea/misc.xml

@@ -1,5 +1,8 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <project version="4">
+  <component name="Black">
+    <option name="sdkName" value="Python 3.11 (quantum-dev)" />
+  </component>
   <component name="MarkdownSettingsMigration">
     <option name="stateVersion" value="1" />
   </component>

ps9-1a.py

@@ -0,0 +1,24 @@
+import numpy as np
+import pylab as pl
+
+a = 1
+n_vals = [n for n in range(1, 7)]
+
+x_vals = np.linspace(-a / 2, a / 2, 1000)
+
+psi_evens = []
+psi_odds = []
+for n in n_vals:
+    if n % 2 == 0:
+        psi_evens.append(np.sqrt(2 / a) * np.sin(n * np.pi * x_vals / a))
+    else:
+        psi_odds.append(np.sqrt(2 / a) * np.cos(n * np.pi * x_vals / a))
+
+pl.title("First 6 Solutions for Infinite Square Well")
+for psi_even in psi_evens:
+    pl.plot(x_vals, psi_even, color='blue')
+for psi_odd in psi_odds:
+    pl.plot(x_vals, psi_odd, color='green')
+pl.vlines([-a / 2, a / 2], ymin=-2, ymax=2, color='red')
+pl.grid()
+pl.show()

ps9-1b.py

@@ -0,0 +1,19 @@
+import numpy as np
+
+a = 1
+n_vals = [n for n in range(1, 7)]
+
+N = 1000
+dx = 1 / N
+x_vals = np.linspace(-a / 2, a / 2, N)
+
+psi_evens = []
+psi_odds = []
+for n in n_vals:
+    if n % 2 == 0:
+        psi_evens.append(np.sqrt(2 / a) * np.sin(n * np.pi * x_vals / a))
+    else:
+        psi_odds.append(np.sqrt(2 / a) * np.cos(n * np.pi * x_vals / a))
+
+for i in range(min(len(psi_evens), len(psi_odds))):
+    print(f'psi_even_{i + 1} * psi_odd_{i + 1} = {np.dot(psi_evens[i], psi_odds[i]) * dx}')

ps9-2.py

@@ -0,0 +1,44 @@
+import numpy as np
+
+a = 1
+hbar = 1.054572e-34
+n_vals = [n for n in range(1, 7)]
+
+N = 1000
+dx = 1 / N
+x_vals = np.linspace(-a / 2, a / 2, N)
+
+psi_funcs = []
+psi_derivs = []
+psi_2nd_derivs = []
+for n in n_vals:
+    if n % 2 == 0:
+        psi_funcs.append(np.sqrt(2 / a) * np.sin(n * np.pi * x_vals / a))
+        psi_derivs.append(np.sqrt(2) * np.pi * n * np.cos(np.pi * n * x_vals / a) / (a * np.sqrt(a)))
+        psi_2nd_derivs.append(
+            -(np.sqrt(2) * np.pi ** 2 * n ** 2 * np.sin(np.pi * n * x_vals / a)) / (a ** 2 * np.sqrt(a)))
+    else:
+        psi_funcs.append(np.sqrt(2 / a) * np.cos(n * np.pi * x_vals / a))
+        psi_derivs.append(-(np.sqrt(2) * np.pi * n * np.sin(np.pi * n * x_vals / a)) / (a * np.sqrt(a)))
+        psi_2nd_derivs.append(
+            -(np.sqrt(2) * np.pi ** 2 * n ** 2 * np.cos(np.pi * n * x_vals / a)) / (a ** 2 * np.sqrt(a)))
+
+print("======= expect_x =======")
+for i in range(len(psi_funcs)):
+    expect_x = np.sum(psi_funcs[i] ** 2 * x_vals) * dx
+    print(f'expect_x_{i + 1} = {expect_x}')
+
+print("======= expect_x^2 =======")
+for i in range(len(psi_funcs)):
+    expect_x_sqrd = np.sum(psi_funcs[i] ** 2 * x_vals ** 2) * dx
+    print(f'expect_x^2_{i + 1} = {expect_x_sqrd}')
+
+print("======= expect_p =======")
+for i in range(len(psi_funcs)):
+    expect_p = np.sum(psi_funcs[i] * 1j * hbar * psi_derivs[i]) * dx
+    print(f'expect_p_{i + 1} = {expect_p}')
+
+print("======= expect_p^2 =======")
+for i in range(len(psi_funcs)):
+    expect_p_sqrd = np.sum(psi_funcs[i] * hbar ** 2 * psi_2nd_derivs[i]) * dx
+    print(f'expect_p^2_{i + 1} = {expect_p_sqrd}')