2s Wavefunction Verification

We start with the assumption that the wave function for the 2s state has the form

where and are to be determined.

The Schrödinger Equation for the s-states of Hydrogen is

and then it is

Assuming that the exponential is eventually going to cancel, provided all goes well, cross multiplying by , and collecting the terms multiplying 1/r, we have

which we re-write as

which works if , so that


Use `me' for the mass of the electron, and `hbar', `Z', `e', and numbers to give a formula for alpha.
Answer for alpha =


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Carl W. David
Department of Chemsitry
University of Connecticut
Storrs, Connecticut 06269-4060
(860)486-3217
david@uconnvm.uconn.edu