Dirac oscillators and quasi-exactly solvable operators. (English) Zbl 1073.81036

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.


81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis
81U15 Exactly and quasi-solvable systems arising in quantum theory
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[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
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