Fix ps16-1

ps16-1.py

@@ -5,7 +5,7 @@ a = 10
 D = 1
 hbar = 1
 m = 1
-zs = np.array([5.963, 2.851, 1.745, 1.124])
+zs = np.array([2.991, 5.98, 8.96, 11.927])
 l = zs / a
 V0 = 2
 
@@ -41,4 +41,5 @@ pl.rcParams['figure.dpi'] = 300
 pl.plot(x, V0_graph)
 for (i, psi) in enumerate(psis):
     pl.plot(x, psi, label=f'psi_odd_{i} z={zs[i]}')
+pl.legend()
 pl.show()

ps16-3.py

@@ -0,0 +1,34 @@
+from typing import Callable
+import numpy as np
+
+z0 = 20
+
+
+def find_root(f: Callable[[float], float], left: float, right: float, tolerance: float = 1e-6,
+              max_iter: int = 100) -> float | None:
+    a = f(left)
+    b = f(right)
+    x = None
+    for _ in range(max_iter):
+        if abs(a - b) < tolerance:
+            break
+        x = left - a * (left - right) / (a - b)
+        y = f(x)
+        if abs(y) < tolerance:
+            break
+        right, b = left, a
+        left, a = x, y
+    return x
+
+
+def cot(x):
+    return 1 / np.tan(x)
+
+
+def func(z: float) -> float:
+    first = np.sqrt((z0 / z) ** 2 - 1)
+    second = cot(z)
+    return first - second
+
+
+print(find_root(func, 6.2, 6.4, max_iter=1000))