Some Aspects of Generalized Contact Interaction in One-Dimensional Quantum Mechanics

Abstract

We construct a one-dimensional contact interaction ($ϵ$ potential) which induces the discontinuity of the wave function while keeping its derivative continuous. By combining the $ϵ$ potential and the Dirac's $\delta$ function, we construct most general one-dimensional contact interactions allowable under the time reversal symmetry. We present some elementary results for the scattering problem which suggest a dual relation between $\delta$ and $ϵ$ potentials.

Comments: Talk presented at The 7th International Conference on Mathematical Results in Quantum Mechanics (Qmath7), June 22-26, 1998, Prague, Czechland