On the quantum dynamics of a point particle in conical space

Abstract

A quantum neutral particle, constrained to move on a conical surface, is used as a toy model to explore bound states due to both a inverse squared distance potential and a $\delta$-function potential, which appear naturally in the model. These pathological potentials are treated with the self-adjoint extension method which yields the correct boundary condition (not necessarily a null wavefunction) at the origin. We show that the usual boundary condition requiring that the wavefunction vanishes at the origin is arbitrary and drastically reduces the number of bound states if used. The situation studied here is closely related to the problem of a dipole moving in conical space.

To appear in Annals of Physics

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• Physical regularization for the spin-1/2 Aharonov-Bohm problem in conical space
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• Remarks on the Aharonov-Casher dynamics in a CPT-odd Lorentz-violating background
• Quantum mechanics of a constrained particle and the problem of prescribed geometry-induced potential
• On the spin-1/2 Aharonov-Bohm problem in conical space: bound states, scattering and helicity nonconservation
• Quantum motion of a point particle in the presence of the Aharonov--Bohm potential in curved space
• On Aharonov-Casher bound states
• Landau levels, self-adjoint extensions and Hall conductivity on a cone
• On the dynamics of a particle on a cone
• Study of electronic properties, Magnetization and persistent currents in a mesoscopic ring by controlled curvature
• Modifications of electron states, magnetization and persistent current in a quantum dot by controlled curvature
• On planar quantum dynamics of a magnetic dipole moment in the presence of electric and magnetic fields
• The centripetal force law and the equation of motion for a particle on a curved hypersurface
• Inertial and topological effects on a 2D electron gas
• Generalized Centripetal Force Law and Quantization of Motion Constrained on 2D Surfaces
• Path Integration in Conical Space
• Self-adjoint extension approach for singular Hamiltonians in (2+1) dimensions
• Dynamics on the cone: closed orbits and superintegrability
• Electronic properties of single and double napped carbon nanocones
• Quantum Mechanics on Sharply Bent Wires via Two-Interval Sturm-Liouville Theory
• Hamiltonian and Lagrangian BRST quantization in Riemann Manifold
• Geometry-induced wavefunction collapse
• Relativistic Quantum Dynamics on a Double Cone
• Hamiltonian and Lagrangian BRST quantization in Riemann Manifold II