#!/usr/bin/env python

"""
This example shows how to work with the Hydrogen radial wavefunctions.
"""

from sympy import var, pprint, Integral, oo, Eq
from sympy.physics.hydrogen import R_nl

def main():
    print "Hydrogen radial wavefunctions:"
    var("r a")
    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()
