Self-adjoint extension approach for singular Hamiltonians in (2+1) dimensions

Abstract

In this work, we review two methods used to approach singular Hamiltonians in (2+1) dimensions. Both methods are based on the self-adjoint extension approach. It is very common to find singular Hamiltonians in quantum mechanics, especially in quantum systems in the presence of topological defects, which are usually modelled by point interactions. In general, it is possible to apply some kind of regularization procedure, as the vanishing of the wave function at the location of the singularity, ensuring that the wave function is square-integrable and then can be associated with a physical state. However, a study based on the self-adjoint extension approach can lead to more general boundary conditions that still gives acceptable physical states. We exemplify the methods by exploring the bound and scattering scenarios of a spin 1/2 charged particle with an anomalous magnetic moment in the Aharonov-Bohm potential in the conical space.

arXiv comment13 pages, 3 figures, matches published version

References in corpus (28)

• CODATA Recommended Values of the Fundamental Physical Constants: 2014
• Self-adjoint extensions of operators and the teaching of quantum mechanics
• Aharonov-Bohm Effect with $\delta$--type Interaction
• The Dirac oscillator in a spinning cosmic string spacetime
• Geometric Phase for Neutral Particle in the Presence of a Topological Defect
• Physical regularization for the spin-1/2 Aharonov-Bohm problem in conical space
• Remarks on the Spectral Properties of Tight Binding and Kronig-Penney Models with Substitution Sequences
• Effects of spin on the dynamics of the 2D Dirac oscillator in the magnetic cosmic string background
• Path integral treatment of two- and three-dimensional delta-function potentials and application to spin-1/2 Aharonov-Bohm problem
• On the quantum dynamics of a point particle in conical space
• On the 2D Dirac oscillator in the presence of vector and scalar potentials in the cosmic string spacetime in the context of spin and pseudospin symmetries
• Effects of Nongauge Potentials on the Spin-1/2 Aharonov-Bohm Problem
• Nonrelativistic quantum dynamics on a cone with and without a constraining potential
• Charged Particle with Magnetic Moment in the Aharonov-Bohm Potential
• Bound states of massive fermions in the Aharonov--Bohm-like fields
• Quantum mechanics of a free particle on a pointed plane revisited
• 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
• Self-adjoint Extension Approach to the spin-1/2 Aharonov-Bohm-Coulomb Problem
• One-Dimensional Semirelativistic Hamiltonian with Multiple Dirac Delta Potentials
• On Aharonov-Casher bound states
• The bound state Aharonov-Bohm effect around a cosmic string revisited
• The attractive nonlinear delta-function potential
• Creation of planar charged fermions in Coulomb and Aharonov-Bohm potentials
• Asymptotic Freedom, Dimensional Transmutation, and an Infra-red Conformal Fixed Point for the $\delta$-Function Potential in 1-dimensional Relativistic Quantum Mechanics
• Comment on "Relativistic Aharonov-Bohm effect in the presence of planar Coulomb potentials"
• Scattering and bound states of a spin--1/2 neutral particle in the cosmic string spacetime
• The spectrum of the Schrödinger Hamiltonian for trapped particles in a cylinder with a topological defect perturbed by two attractive delta interactions

Cited by in corpus (2)

• Observables in Quantum Mechanics and the Importance of Self-adjointness
• Effects of rotation and Coulomb type potential on the spin-1/2 Aharonov-Bohm problem