**Colloquium**

Friday, April 26, 2002

4:00 PM

Physics Building, Room 204

Note special time.

Note special room.

## "A Singular Potential:from Theorist's Toy to Experimental Realization"

**Sidney A. Coon , NSF and New Mexico State University**

[Host: S. Liuti]

ABSTRACT:

The inverse square potential (V(r)~1/r**2), first studied by Cote,
a contemporary of Isaac Newton, is an interesting potential for
nonrelativistic quantum mechanics. It lies on the edge of the line
dividing potentials which can be treated in the familiar manner and those
which are singular. Singular potentials have been studied for a long time
because they can be regarded as models for nonrenormalizable field
theories, and, more recently, as an element of the new paradigm of
effective field theory methods in nuclear physics. In this talk, I will
demonstrate the mathematics of the 1/r**2 potential, including the
anomalous (quantum mechanical) breaking of scale symmetry and a rigorous
treatment of absorption ("fall to the center"). Correct mathematics leads
to a quantum mechanical understanding of the formation of anions
(electrons bound by the dipole moment of a polar molecule) and of a very
recent dedicated experimental study of this potential in the context of
manipulation of cold atoms.

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