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Aharonov–Berry superoscillations in the radial harmonic oscillator potential

Quantum Studies: Mathematics and Foundations volume 7, pages 269–283 (2020)Cite this article

Abstract

In this paper, we study the evolutions of Aharonov–Berry superoscillations under the radial harmonic oscillator potential. For this model, we know the Green function and, taking advantage of it, we use a method recently developed for the step potential to show how superoscillations evolve in time. Also in this case, the time evolution is studied using the notion of super-shift of functions.

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Authors and Affiliations

  1. Schmid College of Science and Technology, Chapman University, Orange, CA, 92866, USA

    D. Alpay

  2. Dipartimento di Matematica, Politecnico di Milano, Via E. Bonardi, 9, 20133, Milan, Italy

    F. Colombo & I. Sabadini

  3. Donald Bren Distinguished Presidential Chair in Mathematics, Chapman University, Orange, CA, 92866, USA

    D. C. Struppa

Authors
  1. D. Alpay
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  2. F. Colombo
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  3. I. Sabadini
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  4. D. C. Struppa
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Correspondence to I. Sabadini.

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Alpay, D., Colombo, F., Sabadini, I. et al. Aharonov–Berry superoscillations in the radial harmonic oscillator potential. Quantum Stud.: Math. Found. 7, 269–283 (2020). https://doi.org/10.1007/s40509-019-00206-5

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  • DOI: https://doi.org/10.1007/s40509-019-00206-5

Keywords

  • Superoscillating functions
  • Convolution operators
  • Schrödinger equation
  • Entire functions with growth conditions

Mathematics Subject Classification

  • 32A15
  • 32A10
  • 47B38