University Physics Notes: Quantum Mechanics – Table of the Radial Parts of Electron Wavefunctions for the Hydrogen
Atom
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.
