Initialisation du repository de Beta

venv/lib/python3.12/site-packages/sympy/physics/tests/test_sho.py

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+from sympy.core import symbols, Rational, Function, diff
+from sympy.physics.sho import R_nl, E_nl
+from sympy.simplify.simplify import simplify
+
+
+def test_sho_R_nl():
+    omega, r = symbols('omega r')
+    l = symbols('l', integer=True)
+    u = Function('u')
+
+    # check that it obeys the Schrodinger equation
+    for n in range(5):
+        schreq = ( -diff(u(r), r, 2)/2 + ((l*(l + 1))/(2*r**2)
+                    + omega**2*r**2/2 - E_nl(n, l, omega))*u(r) )
+        result = schreq.subs(u(r), r*R_nl(n, l, omega/2, r))
+        assert simplify(result.doit()) == 0
+
+
+def test_energy():
+    n, l, hw = symbols('n l hw')
+    assert simplify(E_nl(n, l, hw) - (2*n + l + Rational(3, 2))*hw) == 0