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Spectral analysis and stability properties of a relativistic deformation of the harmonic oscillator. (English) Zbl 0785.34056
Summary: The spectral properties are established and the stability of the eigenvalues under the singular perturbation representing the relativistic corrections are proven for a family of ordinary differential operators describing a relativistic deformation of the quantum harmonic oscillator.
34L40 Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.)
81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
Full Text: DOI
[1] DOI: 10.1006/aphy.1993.1017 · Zbl 0782.47020 · doi:10.1006/aphy.1993.1017
[2] DOI: 10.1103/RevModPhys.21.400 · Zbl 0036.26704 · doi:10.1103/RevModPhys.21.400
[3] Ali S. T., Ann. Inst. H. Poincaré 52 pp 83– (1990)
[4] DOI: 10.1002/qua.560170609 · doi:10.1002/qua.560170609
[5] DOI: 10.1016/0003-4916(85)90305-7 · Zbl 0614.46068 · doi:10.1016/0003-4916(85)90305-7
[6] DOI: 10.1007/BF01976045 · Zbl 0528.35023 · doi:10.1007/BF01976045
[7] DOI: 10.1007/BF01205504 · Zbl 0522.47011 · doi:10.1007/BF01205504
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