A Non-relativistic Approach to Relativistic Quantum Mechanics: The Case of the Harmonic Oscillator

Luis A. Poveda, Luis Grave de Peralta, Jacob Pittman, Bill Poirier

Research output: Contribution to journalArticlepeer-review

Abstract

A recently proposed approach to relativistic quantum mechanics (Grave de Peralta, Poveda, Poirier in Eur J Phys 42:055404, 2021) is applied to the problem of a particle in a quadratic potential. The methods, both exact and approximate, allow one to obtain eigenstate energy levels and wavefunctions, using conventional numerical eigensolvers applied to Schrödinger-like equations. Results are obtained over a nine-order-of-magnitude variation of system parameters, ranging from the non-relativistic to the ultrarelativistic limits. Various trends are analyzed and discussed—some of which might have been easily predicted, others which may be a bit more surprising.

Original languageEnglish
Article number29
JournalFoundations of Physics
Volume52
Issue number1
DOIs
StatePublished - Feb 2022

Keywords

  • Harmonic oscillator
  • Klein–Gordon equation
  • Schrödinger equation
  • Spinless Salpeter equation
  • WKB approximation

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