1. Evolution by Schrödinger equation of Aharonov--Berry superoscillations in centrifugal potential.
- Author
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Colombo, F., Gantner, J., and Struppa, D. C.
- Subjects
- *
EVOLUTION equations , *QUADRATIC equations , *BERRIES , *INTEGRAL functions - Abstract
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. [ABSTRACT FROM AUTHOR]
- Published
- 2019
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