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