Table of Normalized Spherical Harmonics

The Schrodinger equation for the hydrogen atom takes the form

This equation is separable which means that while the solution is a function of three variables, it is a product of three functions, each one of which is a function of only one variable, The general solution can be writtenwhereis itself a product of a function ofandwith a function of the formwhereandare integers.

0

0

1

0

1

2

0

2

2

Notice that in each of theabove the degree of the polynomial inis equal toand there is a complex exponential termwhereis given in the table. There is one uniquefor each combination ofandand obeys the normalization condition

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