For a given principle quantum number
,the largest
radial wavefunction is given by
The radial wavefunctions should be normalized as below.
* Example:
Compute the expected values of , , , and
in the Hydrogen state
.*
The pictures below depict the probability distributions in space for the Hydrogen wavefunctions.
The graphs below show the radial wave functions. Again, for a given the maximum state has no radial excitation, and hence no nodes in the radial wavefunction. As gets smaller for a fixed , we see more radial excitation.
A useful integral for Hydrogen atom calculations is.
* Example:
What is the expectation value of in the state ?*
* Example:
What is the expectation value of in the state ?*
* Example:
What is the expectation value of the radial component of velocity in the state ?*
Jim Branson 2013-04-22