Add ps11-2.13

ps11-2.13-2.py

@@ -0,0 +1,20 @@
+import numpy as np
+import pylab as pl
+
+x_max = 10.0
+x_vals = np.linspace(-x_max, x_max, 1000)
+dx = x_vals[1] - x_vals[0]
+gaussian = np.exp(-x_vals * x_vals / 2)
+
+psi_funcs = [gaussian,
+             x_vals * gaussian,
+             (1 - 2 * x_vals * x_vals) * gaussian,
+             x_vals * (1 - (2.0 / 3.0) * x_vals * x_vals) * gaussian]
+
+for psi in psi_funcs:
+    a = 1.0 / (np.sqrt(psi.dot(psi)) * dx)
+    psi *= a
+
+for psi in psi_funcs:
+    pl.plot(x_vals, psi)
+    pl.show()

ps11-2.13.py

@@ -0,0 +1,45 @@
+import numpy as np
+import pylab as pl
+
+
+def ladder_plus(xs: np.ndarray, psi: np.ndarray) -> np.ndarray:
+    dx = xs[1] - xs[0]
+    return -np.gradient(psi, dx) + xs * psi
+
+
+def ladder_minus(xs: np.ndarray, psi: np.ndarray) -> np.ndarray:
+    dx = xs[1] - xs[0]
+    return np.gradient(psi, dx) + xs * psi
+
+
+def normalize(psi: np.ndarray) -> None:
+    psi /= np.sqrt(np.sum(psi * np.conjugate(psi)))
+
+
+x_vals = np.linspace(-5, 5, 1000)
+
+psi_0 = np.exp(-x_vals ** 2)
+normalize(psi_0)
+
+psi_funcs = [psi_0]
+for i in range(1, 4):
+    psi_next = ladder_plus(x_vals, psi_funcs[i - 1])
+    normalize(psi_next)
+    psi_funcs.append(psi_next)
+
+pl.rcParams['figure.dpi'] = 300
+fig, axs = pl.subplots(2, 2, tight_layout=True)
+fig.tight_layout(pad=2.0)
+axs[0, 0].plot(x_vals, psi_funcs[0])
+axs[0, 0].set_title('ψ0')
+axs[0, 0].grid()
+axs[0, 1].plot(x_vals, psi_funcs[1], 'tab:orange')
+axs[0, 1].set_title('ψ1')
+axs[0, 1].grid()
+axs[1, 0].plot(x_vals, psi_funcs[2], 'tab:green')
+axs[1, 0].set_title('ψ2')
+axs[1, 0].grid()
+axs[1, 1].plot(x_vals, psi_funcs[3], 'tab:red')
+axs[1, 1].set_title('ψ3')
+axs[1, 1].grid()
+pl.show()