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Russian Physics Journal

, Volume 54, Issue 11, pp 1256–1263 | Cite as

Relativistic fermion in a spherically symmetric potential well of finite depth in a two-dimensional space

  • V. Yu. Ananchenko
  • A. V. Sushchevskii
  • M. Sh. Pevzner
  • D. V. Kholod
Article

The problem of existence of bounded relativistic fermion states in a spherically symmetric well of finite depth in a two-dimensional space is investigated. The well depth critical for the appearance of standard states with energies E = m, 0, and –m is determined; moreover, cases with zero and nonzero fermion momenta are considered. Approximate analytical expressions for the critical depths of narrow and wide wells are derived which are in good agreement with the results of numerical calculations. Approximate energies of levels located on the boundaries of the upper and lower continuums and determined analytically are in good agreement with the results of numerical calculations.

Keywords

spherically symmetric potential well bound states two-dimensional space critical well depth 

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Copyright information

© Springer Science+Business Media, Inc. 2012

Authors and Affiliations

  • V. Yu. Ananchenko
    • 1
  • A. V. Sushchevskii
    • 1
  • M. Sh. Pevzner
    • 1
  • D. V. Kholod
    • 1
  1. 1.National Mining University of UkraineDnepropetrovskUkraine

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