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Calculating the expectation of a quantity using wavefunctions 
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#1
Mar912, 05:17 AM

P: 339

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 = e^{2}/r. This implies that the expectation of V = e^{2}/a_{0}n^{2}. Now, I know that you use the unperturbed wavefunction ψ^{0} to find the expectation of V, but I am not sure of the exact form of ψ^{0}. Any help on this will be greatly appreciated. 


#2
Mar912, 05:18 AM

P: 339

I need the form as I want to calculate the expectation myself. Is there a general formula for the wavefunction?



#3
Mar912, 08:55 AM

Sci Advisor
HW Helper
P: 11,893

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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