Explore BrainMass

# First order perturbation in an infinite spherical well

Not what you're looking for? Search our solutions OR ask your own Custom question.

This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

Please see attached question.

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.

© BrainMass Inc. brainmass.com March 5, 2021, 1:35 am ad1c9bdddf
https://brainmass.com/physics/schrodinger/first-order-perturbation-infinite-spherical-well-600559

#### Solution Preview

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 ...

#### 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.

\$2.49