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arXiv · 1601.02390

Two-dimensional Time-dependent Point Interactions

R. Carlone·M. Correggi·R. Figari
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Abstract

We study the time-evolution of a quantum particle subjected to time-dependent zero-range forces in two dimensions. After establishing a conceivable ansatz for the solution to the Schr\"{o}dinger equation, we prove that the wave packet time-evolution is completely specified by the solutions of a system of Volterra-type equations -- the {\it charge equations} -- involving the coefficients of the singular part of the wave function, thus extending to the two-dimensional case known results in one and three dimensions.

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R. Carlone, M. Correggi, R. Figari. 2016-01-11. Two-dimensional Time-dependent Point Interactions. https://doi.org/10.4171/175-1/10

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