Akcay, H.; Tezcan, C. Exact solutions of the Dirac equation with harmonic oscillator potential including a Coulomb-like tensor potential. (English) Zbl 1168.81324 Int. J. Mod. Phys. C 20, No. 6, 931-940 (2009). Summary: We study the Dirac equation with scalar, vector, and tensor interactions. The Dirac Hamiltonian contains quadratic scalar and vector potentials, as well as a tensor potential. The tensor potential is taken as a sum of a linear term and a Coulomb-like term. It is shown that the tensor potential preserves the form of the harmonic oscillator potential and generates spin-orbit terms. The energy eigenvalues and the corresponding eigenfunctions are obtained for different alternatives. Cited in 8 Documents MSC: 81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics 34C40 Ordinary differential equations and systems on manifolds Keywords:Dirac equation; tensor potential; pseudospin symmetry; harmonic oscillator PDFBibTeX XMLCite \textit{H. Akcay} and \textit{C. Tezcan}, Int. J. Mod. Phys. C 20, No. 6, 931--940 (2009; Zbl 1168.81324) Full Text: DOI References: [1] M. Moshinsky, The Harmonic Oscillator in Modern Physics: From Atoms to Quarks (Gordon and Breach, New York, 1969) p. 29. [2] Chen T.-S., Chin. Phys. Lett. 20 pp 358– [3] DOI: 10.1103/PhysRevC.69.024319 · doi:10.1103/PhysRevC.69.024319 [4] DOI: 10.1103/PhysRevC.71.034313 · doi:10.1103/PhysRevC.71.034313 [5] Typel S., Nucl. Phys. A 805 pp 156– [6] DOI: 10.1016/S0375-9474(98)00004-9 · doi:10.1016/S0375-9474(98)00004-9 [7] DOI: 10.1103/PhysRevC.67.044318 · doi:10.1103/PhysRevC.67.044318 [8] DOI: 10.1007/978-1-4757-1595-8 · doi:10.1007/978-1-4757-1595-8 [9] Bjorken J. D., Relativistic Quantum Mechanics (1964) [10] DOI: 10.1103/PhysRevC.69.034318 · doi:10.1103/PhysRevC.69.034318 [11] Serot B. D., Adv. Nucl. Phys. 16 pp 1– [12] DOI: 10.1103/PhysRevLett.91.262501 · doi:10.1103/PhysRevLett.91.262501 [13] DOI: 10.1140/epja/i2006-10066-0 · doi:10.1140/epja/i2006-10066-0 [14] DOI: 10.1016/0375-9601(91)90333-4 · doi:10.1016/0375-9601(91)90333-4 [15] Flügge S., Practical Quantum Mechanics I (1971) · Zbl 1400.81004 [16] DOI: 10.1016/0375-9474(69)90077-3 · doi:10.1016/0375-9474(69)90077-3 [17] DOI: 10.1016/0370-2693(69)90443-2 · doi:10.1016/0370-2693(69)90443-2 [18] DOI: 10.1016/j.physrep.2005.04.003 · doi:10.1016/j.physrep.2005.04.003 [19] DOI: 10.1016/S0370-2693(98)00188-9 · doi:10.1016/S0370-2693(98)00188-9 [20] DOI: 10.1088/0031-8949/26/4/003 · doi:10.1088/0031-8949/26/4/003 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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.