charged particle in external scalar potential

(potential local and non-relativistic)

(no source charges)

Then Note that is an operator. define = electric multipole operator.

- l=0 = total charge
- l=1 = atomic dipole moment

if , the soution will be the same except

Can identify solution with classical solutions:

Cartesian equivalent of l=2: or . symmetric and traceless.

properties:

- for l some value
- in simple quantum systems, for l lmax. e.g. 2 particle system has only 1 2 contributing.
- Noble gases have for all l.

source

psfile jl@crush.caltech.edu index