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arXiv quant-ph/98080341998-08-31quant-phcond-mathep-thnlin.SInucl-thsolv-int

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

Taksu Cheon, T. Shigehara

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

英文摘要：

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 $δ$ 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 $δ$ and $ε$ potentials.

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