The Schrodinger equation for the hydogen 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. The function
depends on
and
The first few functions of
are given in the table below.
|
|
l |
|
|
1 |
0 |
|
|
2 |
0 |
|
|
2 |
1 |
|
|
3 |
0 |
|
|
3 |
1 |
|
|
3 |
2 |
|
The probability of finding the electron at radius
is plotted below for these radial wavefunctions. Each radial wavefunction is normalized to 1.
