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

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

1998-08-20

arxiv.org/abs/quant-ph/9808034v2

Physics

Quantum Physics

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

Scientific paper

We construct a one-dimensional contact interaction ($\epsilon$ potential) which induces the discontinuity of the wave function while keeping its derivative continuous. By combining the $\epsilon$ 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 $\epsilon$ potentials.

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