Free particle and isotropic harmonic oscillator on a spheroidal surface: the Higgs-like approach
arXiv:1808.09175 · doi:10.1063/1.5079468
Abstract
In this paper, we investigate the dynamics of both free particle and isotropic harmonic oscillator constrained to move on a spheroidal surface using two consecutive projections: a projection onto a sphere surface followed by the gnomonic projection onto a tangent plane to the spheroid. We obtain the Hamiltonian of the aforementioned systems in terms of the Cartesian coordinates of the tangent plane and then quantize it in the standard way. It is shown that the effect of non-sphericity of the surface can be treated as the appearance of an effective potential. By using the perturbation theory up to the first order in second eccentricity of the spheroid, we approximately calculate the eigenfunctions and eigenvalues of the free particle, as well as the isotropic harmonic oscillator on the spheroidal surface. We find that the deviation from the sphericity plays an important role in splitting the energy levels of the isotropic oscillator on a sphere, and lifting the degeneracy.
References in corpus (10)
- General Relativity in Electrical Engineering
- The quantum harmonic oscillator on the sphere and the hyperbolic plane
- Effect of the surface curvature on the magnetic moment and persistent currents in two-dimensional quantum rings and dots
- Geometric approach to nonlinear coherent states using the Higgs model for harmonic oscillator
- The quantum free particle on spherical and hyperbolic spaces: A curvature dependent approach
- Coherent state quantization of a particle in de Sitter space
- Hamiltonians for the Quantum Hall Effect on Spaces with Non-Constant Metrics
- Entanglement of two two-levels atoms mediated by an optical black hole
- Two Dimensional Isotropic Harmonic Oscillator on a Time-dependent Sphere
- Quantization of a Particle on a Two-Dimensional Manifold of Constant Curvature