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 written
where
is itself a product of a function of
and
with a function of the form
where
and
are integers.
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1 |
0 |
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1 |
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0 |
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Notice that in each of theabove the degree of the polynomial in
is equal toand there is a complex exponential term
whereis given in the table. There is one uniquefor each combination ofandand obeys the normalization condition