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DIRAC OSCILLATORS AND QUASI-EXACTLY SOLVABLE OPERATORS

Y. BRIHAYE

Department of Mathematical Physics, University of Mons-Hainaut, Place du Parc, B-7000 Mons, Belgium

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and

A. NININAHAZWE

Department of Mathematical Physics, University of Mons-Hainaut, Place du Parc, B-7000 Mons, Belgium

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https://doi.org/10.1142/S0217732305018128Cited by:8 (Source: Crossref)

Abstract

The Dirac equation is formulated in the background of three types of physically relevant potentials: scalar, vector and "Dirac-oscillator" potentials. Assuming these potentials to be spherically-symmetric and with generic polynomial forms in the radial variable, we construct the corresponding radial Dirac equation. Cases where this linear spectral equation is exactly solvable or quasi-exactly solvable are worked out in details. When available, relations between the radial Dirac operator and some super-algebra are pointed out.

Keywords:

PACS: 03.65.Pm, 31.30.Jv

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