The Linear Potential and Harmonic Oscillator in Relativistic Quantum Mechanics

Jacek Karwowski, Grzegorz Pestka

Alexander Davydov

Etido Patrick Inyang, Benedict I. Ita, Etido Patrick Inyang

The solutions of the Klein- Gordon equation for the quantum mechanical gravitational plus harmonic oscillator potential with equal scalar and vector potential have been presented using the parametric Nikiforov-Uvarov method. The energy eigenvalues were obtained in relativistic and non-relativistic regime and the corresponding un-normalized eigenfunctions in terms of Laguerre polynomials. The numerical values for the S – wave bound state were obtained.

Ion I. Cotǎescu, Dumitru N. Vulcanov

Durojaiye Jude Koffa, J. F. Omonile, S. X. K. Howusu

In this paper, the relativistic linear quantum simple harmonic oscillator problem is solved by the method of Fourier Hermite series to derive the exact analytical solutions of the relativistic linear quantum simple harmonic oscillator. The first profound physical result of this work is the discovery of indefinitely fine corrections to the well known sequence of Schrodinger's quantum mechanical eigenenergies which become significant as the oscillator moves faster and faster compared to the speed of light in vacuo, especially the subatomic and elementary particles. the result implies corresponding hitherto unknown results in the areas of theoretical and experimental physics of oscillations and vibrations, such as Solid State Physics, Statistical and Thermal Physics and Particle Physics.

Owen L. de Lange, R. E. Raab

Preface The mathematical formalism of quantum mechanics The harmonic oscillator Other one-dimensional systems Angular momentum Spherically symmetric potentials Applications Factorization with application to the momentum representation The isotropic harmonic oscillator in an angular momentum basis The Coulomb problem in an angular momentum basis The Coulomb problem in the basis /HA OzL Tz Relativistic quantum mechanics Relativistic spherically symmetric problems References Appendices.