Brihaye, Y.; Nininahazwe, A. Dirac oscillators and quasi-exactly solvable operators. (English) Zbl 1073.81036 Mod. Phys. Lett. A 20, No. 25, 1875-1885 (2005). Summary: 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. Cited in 2 Documents MSC: 81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis 81U15 Exactly and quasi-solvable systems arising in quantum theory Keywords:Exact and quasi-exact solvability; Dirac equation PDF BibTeX XML Cite \textit{Y. Brihaye} and \textit{A. Nininahazwe}, Mod. Phys. Lett. A 20, No. 25, 1875--1885 (2005; Zbl 1073.81036) Full Text: DOI arXiv References: [1] DOI: 10.1007/BF01466727 · Zbl 0683.35063 [2] Ushveridze A. G., Quasi Exact Solvability in Quantum Mechanics (1993) [3] Turbiner A. V., Phys. Rev. 50 pp 5335– [4] Brihaye Y., Mod. Phys. Lett. 14 pp 2579– [5] Znojil M., Mod. Phys. Lett. 14 pp 863– [6] DOI: 10.1016/j.aop.2004.01.007 · Zbl 1045.81017 [7] DOI: 10.1007/BF02125129 · Zbl 0696.35183 [8] Lin Q.-G., J. Phys. 25 pp 1795– [9] DOI: 10.1063/1.531034 · Zbl 0842.35096 [10] DOI: 10.1063/1.532028 · Zbl 0879.35129 [11] DOI: 10.1063/1.1418426 · Zbl 1059.81037 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.