Estimating Ground State Energy Correction of Hydrogenic Atom

[eman2009]

Homework Statement

using first-order perturbation theory ,estimate the correction to the ground state energy of a hydrogenic atom due to the finite size of the nucleus, assume it's spherical nucleus.

Homework Equations

you can employ the fact that the electrostatic potential fi
fi=Ze/R(3/2-r^/2R^ ,if r<R

=Ze/r ,if r>R

fi is elctrostatic potential

R is radius, chargeZe

The Attempt at a Solution

 

[orthovector]

think Bohr radius A_o = Bohr radius

 

[malawi_glenn]

can you please write down the potential "fi" more clear?

is it

\phi = \frac{Ze(3/2 -r^2/(2R^2))}{R} ?? or

\phi = \frac{Ze}{R(3/2 -r^2/(2R^2)}

Also show attempt to solution, you have to show some effort in order to get help. Read the rules of this forum.

 

[eman2009]

sorry
the second one is
fi=Ze/r only
and the first one is correct
there is two equation for fi ...

i tryed to treat (fi) as (V) ,my question is how i can applay the perturbation theory in the same time using radial equation ? if i use perturbation theory what is (ebsay)
is it
1/(squarbi a^3).e^-r/a
for ground state
thanks

 

[eman2009]

please answer me ...

 

[eman2009]

i don't know what happen ... some thing wrong ):