Some Aspects of Generalized Contact Interaction in One-Dimensional Quantum Mechanics
Taksu Cheon, T. Shigehara
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 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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