Relativistic Harmonic Oscillator

Abstract

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.

14 pages, extended discussion of results

References in corpus (10)

• Energy bounds for the spinless Salpeter equation: harmonic oscillator
• Discrete Spectra of Semirelativistic Hamiltonians
• Discrete spectra of semirelativistic Hamiltonians from envelope theory
• Relativistic N-boson systems bound by pair potentials V(r_{ij}) = g(r_{ij}^2)
• Energy bounds for the spinless Salpeter equation
• Convexity and potential sums for Salpeter-like Hamiltonians
• Relativistic N-Boson Systems Bound by Oscillator Pair Potentials
• Lower bounds for the spinless Salpeter equation
• The energy of a system of relativistic massless bosons bound by oscillator pair potentials
• Spinless Salpeter Equation: Some (Semi-) Analytical Approaches

Cited by in corpus (22)

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• The Salpeter equation and probability current in the relativistic Hamiltonian quantum mechanics
• The relativistic massless harmonic oscillator
• Levy flights and nonlocal quantum dynamics
• Experimental Realization of a Relativistic Harmonic Oscillator
• Solving fractional Schroedinger-type spectral problems: Cauchy oscillator and Cauchy well
• Exact Solutions of Bethe-Salpeter Equations with Instantaneous Interactions
• The modified fundamental equations of quantum mechanics
• Semirelativistic Hamiltonians and the auxiliary field method
• The auxiliary field method in quantum mechanics
• A new representation for non--local operators and path integrals
• New results by low momentum approximation from relativistic quantum mechanics equations and suggestion of experiments
• Relativistic chaos in the anisotropic harmonic oscillator
• Bound state equivalent potentials with the Lagrange mesh method
• On the coherent states for a relativistic scalar particle
• The Spinless Relativistic Kink-Like Problem
• Relativistic Ermakov-Milne-Pinney Systems and First Integrals
• Ultrarelativistic bound states in the spherical well
• Nonlocally-induced (quasirelativistic) bound states: Harmonic confinement and the finite well
• Timeless Relativistic Approach to Classical Mechanics
• QuantumFDTD -- A computational framework for the relativistic Schrödinger equation
• Relativistic Langevin Equation derived from a particle-bath Lagrangian