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Problem on perturbation theory

  1. Oct 19, 2007 #1
    1. The problem statement, all variables and given/known data
    Determine approximately the ground state energy of a helium like atom using first order perturbation theory in the electron-electron interaction.
    Ignore the spins of the electrons and the Pauli principle.

    2. Relevant equations
    given that [tex]\int[/tex]d[tex]\tau[/tex]1[tex]\int[/tex]d[tex]\tau[/tex]2 e[tex]^-(r1+r2){}[/tex]/r1+r2 = 20[tex]\Pi[/tex][tex]^{2}[/tex]

    3. The attempt at a solution
    Consider a system where electron1-electron2 distance = r12
    electron1-nucleus distance= r1
    electron2-nucleus distance= r2

    The S.E of this system would be exactly solvable if the term containing r12 disappears from the hamiltonian. Therefore we treat k/(r12)[tex]^{2}[/tex] as the perturbation!

    I applied the first order perturbation for the term k/r12
    the correction would basically be <[tex]\Psi[/tex] /k/(r12)[tex]^{2}[/tex] / [tex]\Psi[/tex]>

    And i am stuck! Cant understand what to do next!
  2. jcsd
  3. Oct 19, 2007 #2


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    Staff Emeritus
    Science Advisor
    Gold Member

    Can you write down the perturbing and unperturbed hamiltonia, and the eigenfunctions of the unperturbed hamiltonian?

    Why are you squaring r12?

    PS: When writing down an expression/equation, it is best to LaTeX the whole thing (Example: [itex]\langle \psi | (k/r_{12})| \psi \rangle [/itex]), rather than parts of it. Also, for using LaTeX in line with regular text, use the tags [ itex ] [ /itex ] (without spaces) instead.
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