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Homework Help: How to use extra term in radial equation

  1. Apr 28, 2007 #1
    1. The problem statement, all variables and given/known data

    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

    2. Relevant equations

    Radial equation


    Eigenenergies for hydrogen atom


    3. 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


    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?

  2. jcsd
  3. Apr 28, 2007 #2
    My feeling is that you could rescale the r-axis to get this problem solved.
    The additional term in the potential is similar to the angular momentum term.
    Therefore, the effect should be equivalent to the same problem with r rescaled and V(r) rescaled correspondingly.
    But that is only my guess ...
    Hope it helps.
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