#NEWLINE# def main( ) : #NEWLINE# #INDENT# print ( 'Hydrogen radial wavefunctions:' ) #NEWLINE# ( a , r ) = symbols ( 'a r' ) #NEWLINE# print ( 'R_{21}:' ) #NEWLINE# pprint ( R_nl ( 2 , 1 , a , r ) ) #NEWLINE# print ( 'R_{60}:' ) #NEWLINE# pprint ( R_nl ( 6 , 0 , a , r ) ) #NEWLINE# print ( 'Normalization:' ) #NEWLINE# i = Integral ( ( ( R_nl ( 1 , 0 , 1 , r ) ** 2 ) * ( r ** 2 ) ) , ( r , 0 , oo ) ) #NEWLINE# pprint ( Eq ( i , i . doit ( ) ) ) #NEWLINE# i = Integral ( ( ( R_nl ( 2 , 0 , 1 , r ) ** 2 ) * ( r ** 2 ) ) , ( r , 0 , oo ) ) #NEWLINE# pprint ( Eq ( i , i . doit ( ) ) ) #NEWLINE# i = Integral ( ( ( R_nl ( 2 , 1 , 1 , r ) ** 2 ) * ( r ** 2 ) ) , ( r , 0 , oo ) ) #NEWLINE# pprint ( Eq ( i , i . doit ( ) ) )