code: def test_wavefunction():
      a = 1 / Z
      R = {
          (1, 0): 2 * sqrt(1 / a**3) * exp(-r / a),
          (2, 0): sqrt(1 / (2 * a**3))
          * exp(-r / (2 * a))
          * (1 - r / (2 * a)),
          (2, 1): S.Half
          * sqrt(1 / (6 * a**3))
          * exp(-r / (2 * a))
          * r
          / a,
          (3, 0): Rational(2, 3)
          * sqrt(1 / (3 * a**3))
          * exp(-r / (3 * a))
          * (1 - 2 * r / (3 * a) + Rational(2, 27) * (r / a) ** 2),
          (3, 1): Rational(4, 27)
          * sqrt(2 / (3 * a**3))
          * exp(-r / (3 * a))
          * (1 - r / (6 * a))
          * r
          / a,
          (3, 2): Rational(2, 81)
          * sqrt(2 / (15 * a**3))
          * exp(-r / (3 * a))
          * (r / a) ** 2,
          (4, 0): Rational(1, 4)
          * sqrt(1 / a**3)
          * exp(-r / (4 * a))
          * (
              1
              - 3 * r / (4 * a)
              + Rational(1, 8) * (r / a) ** 2
              - Rational(1, 192) * (r / a) ** 3
          ),
          (4, 1): Rational(1, 16)
          * sqrt(5 / (3 * a**3))
          * exp(-r / (4 * a))
          * (1 - r / (4 * a) + Rational(1, 80) * (r / a) ** 2)
          * (r / a),
          (4, 2): Rational(1, 64)
          * sqrt(1 / (5 * a**3))
          * exp(-r / (4 * a))
          * (1 - r / (12 * a))
          * (r / a) ** 2,
          (4, 3): Rational(1, 768)
          * sqrt(1 / (35 * a**3))
          * exp(-r / (4 * a))
          * (r / a) ** 3,
      }
      for n, l in R:
          assert simplify(R_nl(n, l, r, Z) - R[(n, l)]) == 0
  
file_path: sympy/sympy/physics/tests/test_hydrogen.py
imports: from sympy.core.numbers import I, Rational, oo, pi
  from sympy.core.singleton import S
  from sympy.core.symbol import symbols
  from sympy.functions.elementary.exponential import exp
  from sympy.functions.elementary.miscellaneous import sqrt
  from sympy.functions.elementary.trigonometric import cos, sin
  from sympy.integrals.integrals import integrate
  from sympy.simplify.simplify import simplify
  from sympy.physics.hydrogen import R_nl, E_nl, E_nl_dirac, Psi_nlm
  from sympy.testing.pytest import raises
label_desc: Use image node_id 2 for calling a global function with example usage: test_wavefunction() without return types