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Homework Help: Multipolar Polarization

  1. Mar 3, 2007 #1
    1. The problem statement, all variables and given/known data
    Using the explicit expression for the mulitpolar polarization, find the matrix elements <2s | P(r) | 1s> of the microscopic polarization between the 1s and 2s states of the hydrogen atom.

    2. Relevant equations
    [tex]P(r) = \int dr' r' \rho(r') \delta(r-r')[/tex]

    I don't understand how the Dirac Delta Function is supposed work? What it is and how does it operate in the intergral?

    3. The attempt at a solution
    [tex]<\psi(2s) | P(r) | \psi(1s) = \int dr' r' \rho(r') \delta(r-r')[/tex]

    [tex]\psi(1s), \psi(2s)[/tex] are just H-atom wavefunctions.
  2. jcsd
  3. Mar 4, 2007 #2
    I'm not familiar with this operator, but just looking at the equation for P(r) I would read it as rho(r)*r. The delta function restricts the integrand to the point where r' = r, and it's equal to zero for other values of r'.
  4. Mar 13, 2007 #3
    This is easy!
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