Quantization of the conformal Kepler problem and its application to the hydrogen atom

DOI10.1063/1.525473zbMath0489.58015OpenAlexW1980939711MaRDI QIDQ3951275

Toshihiro Iwai

Publication date: 1982

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.525473

zbMATH Keywords

energy levelsquantum operatorquantization of the conformal Kepler problemreduction of the 4-dimensional conformal hydrogen atom to the 3-dimensional ordinary hydrogen atomsymmetry groups of the conformal hydrogen atom

Mathematics Subject Classification ID

General quantum mechanics and problems of quantization (81S99) Applications of quantum theory to specific physical systems (81V99) Geometric quantization (53D50)

Related Items

An integrable model of a planar tri-atomic molecule, Dirac Particle in the Coulomb Field on the Background of Hyperbolic Lobachevsky Model, Coulomb-oscillator duality in spaces of constant curvature, REDUCTION AND UNFOLDING FOR QUANTUM SYSTEMS: THE HYDROGEN ATOM, A gauge theory for the quantum planar three-body problem, Normalization and the detection of integrability: The generalized van der Waals potential, The quantized \(\text{SU}(2)\) Kepler problem and its symmetry group for negative energies, The symmetry group of the harmonic oscillator and its reduction

Cites Work

• On the derivation of the Schrödinger equation in a Riemannian manifold
• Quantization of Nonlinear Systems
• Quantization on a manifold with connection
• On a ‘‘conformal’’ Kepler problem and its reduction
• On reduction of the four-dimensional harmonic oscillator
• The symmetry group of the harmonic oscillator and its reduction
• Space-Time Approach to Non-Relativistic Quantum Mechanics
• Dynamical Theory in Curved Spaces. I. A Review of the Classical and Quantum Action Principles