Calculating the expectation of a quantity using wavefunctions


by failexam
Tags: expectation, quantity, wavefunctions
failexam
failexam is offline
#1
Mar9-12, 05:17 AM
P: 338
I am reading the fine structure article from Wikipedia at http://en.wikipedia.org/wiki/Fine_structure.

Under the heading 'Kinetic energy relativistic correction', we have the following:

For the hydrogen atom, V = e2/r. This implies that the expectation of V = -e2/a0n2.

Now, I know that you use the unperturbed wavefunction ψ0 to find the expectation of V, but I am not sure of the exact form of ψ0. Any help on this will be greatly appreciated.
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failexam
failexam is offline
#2
Mar9-12, 05:18 AM
P: 338
I need the form as I want to calculate the expectation myself. Is there a general formula for the wavefunction?
dextercioby
dextercioby is offline
#3
Mar9-12, 08:55 AM
Sci Advisor
HW Helper
P: 11,863
Usually the expectation value is computed with the ground state wavefunction. You can find the n=1, l=0, m=0 wavefunction in any book on QM.


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