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Bi-Confluent Heun Potentials for a Stationary Relativistic Wave Equation for a Spinless Particle

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Journal of Contemporary Physics (Armenian Academy of Sciences) Aims and scope

Abstract

The variety of bi-confluent Heun potentials for a stationary relativistic wave equation for a spinless particle is presented. The physical potentials and energy spectrum of this wave equation are related to those for a corresponding Schrödinger equation in the sense that all the potentials derived for the latter equation are also applicable for the wave equation under consideration. We show that in contrast to the Schrödinger equation the characteristic spatial length of the potential imposes a restriction on the energy spectrum that directly reflects the uncertainty principle. Studying the inversesquare- root bi-confluent Heun potential, it is shown that the uncertainty principle limits, from below, the principal quantum number for the bound states, i.e., physically feasible states have an infimum cut so that the ground state adopts a higher quantum number as compared to the Schrödinger case.

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Authors and Affiliations

  1. Russian–Armenian University, Yerevan, Armenia

    H. H. Azizbekyan, A. M. Manukyan, V. M. Mekhitarian & A. M. Ishkhanyan

  2. Institute for Physical Research, NAS of Armenia, Ashtarak, Armenia

    H. H. Azizbekyan, A. M. Manukyan, V. M. Mekhitarian & A. M. Ishkhanyan

  3. Armenian State Abovyan Pedagogical University, Yerevan, Armenia

    A. M. Ishkhanyan

Authors
  1. H. H. Azizbekyan
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  2. A. M. Manukyan
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  3. V. M. Mekhitarian
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  4. A. M. Ishkhanyan
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Corresponding author

Correspondence to A. M. Ishkhanyan.

Additional information

Original Russian Text © H.H. Azizbekyan, A.M. Manukyan, V.M. Mekhitarian, A.M. Ishkhanyan, 2018, published in Izvestiya Natsional'noi Akademii Nauk Armenii, Fizika, 2018, Vol. 53, No. 4, pp. 373–381.

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Azizbekyan, H.H., Manukyan, A.M., Mekhitarian, V.M. et al. Bi-Confluent Heun Potentials for a Stationary Relativistic Wave Equation for a Spinless Particle. J. Contemp. Phys. 53, 279–285 (2018). https://doi.org/10.3103/S1068337218040023

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  • DOI: https://doi.org/10.3103/S1068337218040023

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