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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 4 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
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References:

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