Physics of singular points in quantum mechanics

Details Physics of singular points in quantum mechanics Physics of singular points in quantum mechanics

2003-12-03

arxiv.org/abs/quant-ph/0312028v1

Physics

Quantum Physics

Latex, 18 pages, 8 figures; for the proceedings of the conference Non-locality of Quantum Mechanics and Statistical Inference,

Scientific paper

Defects or junctions in materials serve as a source of interactions for particles, and in idealized limits they may be treated as singular points yielding contact interactions. In quantum mechanics, these singularities accommodate an unexpectedly rich structure and thereby provide a variety of physical phenomena, especially if their properties are controlled properly. Based on our recent studies, we present a brief review on the physical aspects of such quantum singularities in one dimension. Among the intriguing phenomena that the singularities admit, we mention strong vs weak duality, supersymmetry, quantum anholonomy (Berry phase), and a copying process by anomalous caustics. We also show that a partition wall as a singularity in a potential well can give rise to a quantum force which exhibits an interesting temperature behavior characteristic to the particle statistics.

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