First order perturbation in an infinite spherical well
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Update: The correction is due to relativistic effects.
-(1/2mc^2)(E^2-2E[V]+[V^2])
Where [V] is the expectation value of the potential
I updated the question. Please let me know if you need more.
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Solution Summary
The solution shows how to obtain the wave functions of an infinite spherical well for l=0 modes. It then goes on calculating the energies and the first order corrections due to perturbation.
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The standard radial equation for the radial wave function is:
(1.1)
Then for l=0 and for the region where V=0 we get:
(1.2)
Using the substitution we obtain:
(1.3)
After simplifying it simply becomes:
(1.4)
We define
(1.5)
Then the solution of the harmonic equation is:
(1.6)
If we do a little coordination transformation we see that
(1.7)
Only now, instead of having (due to the infinite potential ...
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