Multipolar Polarization

  • #1

Homework Statement

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.

Homework 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?

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.

Answers and Replies

  • #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'.
  • #3
This is easy!

Suggested for: Multipolar Polarization