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valtorEN
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Homework Statement
Due to the modification of inner-shell electrons of a multi-electron system,
the outer shell electron can feel an effective electrostatic potential as
V(r)=-e^2/(4*π*eo*R)-lambda*(e^2/(4*π*eo*R^2)) ; 0<lambda≤1
Find the energy eigenvalues and wavefunctions of the outer shell electron
and compare to those of the hydrogen atom
Homework Equations
Radial equation
-hbar^2/2*m(d^2u/dr^2)+[(V(r)+(hbar^2/2*m)*l(l+1)/R^2]
Eigenenergies for hydrogen atom
En=-[(m/2*hbar^2)*(e^2/4*π*e0)^2]*(1/n^2)=E1/n^2
The Attempt at a Solution
i plugged the effective potential into the radial equation, divided by E
(E=-hbar^2*k^2/(2*m)) where k=sqrt(2mE)/hbar
and get an equation with the same general solutions as in my book
u(rho)=(rho^(l+1))*(e^(-rho))*(v(rho))
still, how does this term effect the energy compared to that with hydrogen's
eigenenergies? i assume a const term with lambda in it finds it way into the
eigenenergies, but how to solve this is beyond me!
how do i calculate the new energy eigenvalues and wave functions?
how do they compare to that of hydrogen?
cheers
nate