Quantum Mechanics Model on Kähler conifold

Abstract

We propose an exactly-solvable model of the quantum oscillator on the class of Kähler spaces (with conic singularities), connected with two-dimensional complex projective spaces. Its energy spectrum is nondegenerate in the orbital quantum number, when the space has non-constant curvature. We reduce the model to a three-dimensional system interacting with the Dirac monopole. Owing to noncommutativity of the reduction and quantization procedures, the Hamiltonian of the reduced system gets non-trivial quantum corrections. We transform the reduced system into a MIC-Kepler-like one and find that quantum corrections arise only in its energy and coupling constant. We present the exact spectrum of the generalized MIC-Kepler system. The one-(complex) dimensional analog of the suggested model is formulated on the Riemann surface over the complex projective plane and could be interpreted as a system with fractional spin.

5 pages, RevTeX format, some misprints heve been corrected

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Cited by in corpus (16)

• Quantum Oscillator on $\DC P^n$ in a constant magnetic field
• Relationship between quantum mechanics with and without monopoles
• Second Hopf map and Yang-Coulomb system on 5d (pseudo)sphere
• Hamiltonian reduction and supersymmetric mechanics with Dirac monopole
• Three dimensional N=4 supersymmetric mechanics with Wu-Yang monopole
• Elements of (super-)Hamiltonian Formalism
• Hyperboloid, instanton, oscillator
• Supersymmetric Kähler oscillator in a constant magnetic field
• Isospin particle systems on quaternionic projective spaces
• Two--center quantum MICZ--Kepler system and the Zeeman effect in the charge-dyon system
• N=4 chiral supermultiplet interacting with a magnetic field
• Dipole transitions and Stark effect in the charge-dyon system
• Self-Adjointness of Generalized MIC-Kepler System
• Quantum oscillator on complex projective space (Lobachewski space) in constant magnetic field and the issue of generic boundary conditions
• Generalized Solutions for Quantum Mechanical Oscillator on Kähler Conifold
• Generalized MICZ-Kepler systems on three-dimensional sphere and hyperboloid