Evolution by Schrödinger equation of Aharonov–Berry superoscillations in centrifugal potential
2019 ◽
Vol 475
(2225)
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pp. 20180390
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Keyword(s):
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.
2005 ◽
Vol 133
(07)
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pp. 1993-2003
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2006 ◽
Vol 08
(04)
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pp. 433-452
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2012 ◽
Vol 10
(3)
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pp. 927-941
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2011 ◽
Vol 377
(1)
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pp. 420-427
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Keyword(s):
2005 ◽
Vol 216
(1)
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pp. 188-222
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2007 ◽
Vol 143
(2)
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pp. 2857-2868
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