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Evolution by Schrödinger equation of Aharonov-Berry superoscillations in centrifugal potential. (English) Zbl 1472.35321

Summary: In recent years, we have investigated the evolution of superoscillations under Schrödinger equation with non-singular potentials. In all those cases, we have shown that superoscillations persist in time. In this paper, we investigate the centrifugal potential, which is a singular potential, and we show that the techniques developed to study the evolution of superoscillations in the case of the Schrödinger equation with a quadratic Hamiltonian apply to this setting. We also specify, in the case of the centrifugal potential, the notion of super-shift of the limit solution, a fact explained in the last section of this paper. It then becomes apparent that superoscillations are just a particular case of super-shift.

MSC:

35Q41 Time-dependent Schrödinger equations and Dirac equations
47F05 General theory of partial differential operators
30D35 Value distribution of meromorphic functions of one complex variable, Nevanlinna theory
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