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Self-Similar Potentials in Quantum Mechanics and Coherent States

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Abstract

A brief description of the relations between the factorization method in quantum mechanics, self-similar potentials, integrable systems and the theory of special functions is given. New coherent states of the harmonic oscillator related to the Fourier transformation are constructed.

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Funding

This work is partially supported by the Laboratory of Mirror Symmetry NRU HSE, RF government grant, ag. no. 14.641.31.0001.

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Authors and Affiliations

  1. Laboratory of theoretical physics, JINR, Dubna; National Research University Higher School of Echonomics, Moscow, Russia

    V. P. Spiridonov

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  1. V. P. Spiridonov
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Correspondence to V. P. Spiridonov.

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To the blessed memory of V.B. Priezzhev

Based on the talk given at the seminar “In the search of beauty: from condensed matter to integrable systems”, dedicated to V.B. Priezzhev, 10 September 2019, BLTP JINR; http:// thproxy.jinr.ru/video/seminars/2019-09-10/mp4/

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Spiridonov, V.P. Self-Similar Potentials in Quantum Mechanics and Coherent States. Phys. Part. Nuclei 52, 274–289 (2021). https://doi.org/10.1134/S1063779621020052

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