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 δ-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.

Path integration in conical space

“…The conical topology also occurs in (2+1)-dimensional Einstein gravity with localized masses [13]. In this connection, the Schrödinger equation in conical space has been further discussed in [14] - [16].…”

Discrete Energy Spectrum for a Spin-1/2 Quantum Particle Under the Influence of a Constant Force Field due to the Presence of Topological Defects

“…Recently, linear topological defects have been studied by the KatanaevVolovich approach [1] in such systems as circular orbits [3][4][5], quantum scattering problems [6], bound states [7][8][9], and in the analog of the Aharonov-Bohm effect K. Bakke (B) Departamento de Física, Universidade Federal da Paraíba, Caixa Postal 5008, 58051-970, João Pessoa, Paraiba, Brazil e-mail: kbakke@fisica.ufpb.br for bound states [10][11][12]. The study of the influence of linear topological defects has been extended to the interaction between the topological defect and the harmonic oscillator [13,14], the application of the selfadjoint extension method [15][16][17], geometric phases for neutral particles [18][19][20][21][22][23], the Landau quantization for a charged particle and a neutral particle [24][25][26][27][28][29][30], and the Holonomic quantum computation [31,32]. An interesting work [33] has established an analogy between a uniform distribution of parallel screw dislocations and a uniform magnetic field, shown that Landau quantization can be achieved and coined the expression "elastic Landau quantization" [33].…”

The centripetal force law and the equation of motion for a particle on a curved hypersurface

“…The motion of a particle on a curved hypersurface is an exactly solvable model to examine various problems such as higher-dimensional gravity [1], the dark energy/matter problem [2], the quantization of constrained motions for a nonrelativistic particle [3][4][5][6][7] and for a relativistic fermion [8,9], and many curvature-induced effects in lower-dimensional systems and nanostructures [10][11][12][13][14][15], etc. We are familiar with both the geodesic equation from the intrinsically curved surface and the equation of motion from the extrinsically Euclidean space [5,6], but no relationship in between has been seriously explored.…”