Phy5645/Hydrogen Atom WKB

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The WKB approximation is given by

where

We may rewrite the above as

or, making the substitution,

and

Using the fact that and that

we obtain

We now observe that so that

and

We thus obtain

or

This equation simplifies to

We may now easily solve for obtaining

Note that this is exactly the spectrum that we would obtain from an exact solution of the Coulomb problem.

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