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#!/usr/bin/env python
"""
This example shows how to work with the Hydrogen radial wavefunctions.
"""
from sympy import Eq, Integral, oo, pprint, symbols
from sympy.physics.hydrogen import R_nl
def main():
print("Hydrogen radial wavefunctions:")
a, r = symbols("a r")
print("R_{21}:")
pprint(R_nl(2, 1, a, r))
print("R_{60}:")
pprint(R_nl(6, 0, a, r))
print("Normalization:")
i = Integral(R_nl(1, 0, 1, r)**2 * r**2, (r, 0, oo))
pprint(Eq(i, i.doit()))
i = Integral(R_nl(2, 0, 1, r)**2 * r**2, (r, 0, oo))
pprint(Eq(i, i.doit()))
i = Integral(R_nl(2, 1, 1, r)**2 * r**2, (r, 0, oo))
pprint(Eq(i, i.doit()))
if __name__ == '__main__':
main()
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