Energy-dependent point interactions in one dimension
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Iop Publishing Ltd
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We consider a new type of point interaction in one-dimensional quantum mechanics. It is characterized by a boundary condition at the origin that involves the second and/or higher order derivatives of the wavefunction. The interaction is effectively energy dependent. It leads to a unitary S-matrix for the transmission-reflection problem. The energy dependence of the interaction can be chosen such that any given unitary S-matrix (or the transmission and reflection coefficients) can be reproduced at all energies. Generalization of the results to coupled-channel cases is discussed.
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Journal of Physics A-mathematical and General. Bristol: Iop Publishing Ltd, v. 38, n. 22, p. 4989-4998, 2005.
