Relativistic harmonic oscillator

Relativistic harmonic oscillator

We study the semirelativistic Hamiltonian operator composed of the relativistic kinetic energy and a static harmonic-oscillator potential in three spatial dimensions and construct, for bound states with vanishing orbital angular momentum, its eigenfunctions in “compact form,” i.e., as power series,...

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Veröffentlicht in:Journal of mathematical physics 2005-10, Vol.46 (10), p.103514-103514-11
Hauptverfasser: Li, Zhi-Feng, Liu, Jin-Jin, Lucha, Wolfgang, Ma, Wen-Gan, Schöberl, Franz F.
Format: Artikel
Sprache:eng
Schlagworte:
BOUND STATE
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
EIGENFUNCTIONS
EIGENVALUES
Exact sciences and technology
HAMILTONIANS
HARMONIC OSCILLATORS
KINETIC ENERGY
Mathematical methods in physics
MATHEMATICAL SOLUTIONS
Mathematics
ORBITAL ANGULAR MOMENTUM
Physics
POTENTIALS
POWER SERIES
QUANTUM MECHANICS
RELATIVISTIC RANGE
Sciences and techniques of general use
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Beschreibung
Zusammenfassung:We study the semirelativistic Hamiltonian operator composed of the relativistic kinetic energy and a static harmonic-oscillator potential in three spatial dimensions and construct, for bound states with vanishing orbital angular momentum, its eigenfunctions in “compact form,” i.e., as power series, with expansion coefficients determined by an explicitly given recurrence relation. The corresponding eigenvalues are fixed by the requirement of normalizability of the solutions.
ISSN:0022-2488
1089-7658
DOI:10.1063/1.2054648