Relativistic Generalizations of the Quantum Harmonic Oscillator
A. Poszwa
Department of Physics and Computer Methods, University of Warmia and Mazury in Olsztyn, SĹ‚oneczna 54, 10-710 Olsztyn, Poland
Received: March 27, 2014
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We investigate the dynamics of the spin-less relativistic particle subject to an external field of a harmonic oscillator potential. The Klein-Gordon equation with one- and three-dimensional vector and scalar parabolic potentials is solved using the expansion of the wavefunction in properly selected basis-sets. The resonance states are determined using the complex coordinate rotation method. The analytic expressions for the first- and second-order relativistic energy corrections are derived perturbatively. The relativistic model of the harmonic oscillator in the momentum representation, originally proposed by Znojil, is also discussed.

DOI: 10.12693/APhysPolA.126.1226
PACS numbers: 03.65.-w