Delta function potentials in two-dimensional and three-dimensional quantum mechanics

Kok An Wong, Su-Long Nyeo

D. K. Park

Delta-function potentials in two- and three-dimensional quantum mechanics are analyzed by incorporating the self-adjoint extension method within the Green’s-function method. The energy-dependent Green’s functions for free particle plus delta-function potential systems are explicitly determined and similar calculations are carried out for the spin-1/2 Aharonov–Bohm system. It is found that the time-dependent propagator for the latter cannot be evaluated analytically except for a particular value of the self-adjoint extension parameter. It corresponds to the case in which the singular solution alone contributes for the partial wave defined by ‖m+α‖<1.

S. Brandt, Hans Dieter Dahmen

HE Dong-hui

The quantum mechanics of a bound particle in the delta-function potential in three dimensions is studied with a discussion of its regularization and renormalization.A simple regularization approach is considered with introduction of several regularizing functions for defining the quantum system.Furthermore,more systematic regularization is introduced from the mathematical viewpoint of the theory of distributions.

I. Richard Lapidus

Scattering lengths are obtained for the scattering of particles from two-dimensional circular barrier, hard circle, and delta function ring potentials using classical mechanics and quantum mechanics. These results will be of interest in a quantum mechanics course as a supplement to the discussion of three-dimensional scattering.

S. Brandt, Hans Dieter Dahmen