Quantum mechanics of a constrained particle and the problem of prescribed geometry-induced potential

DOI10.1016/j.aop.2017.02.012zbMath1365.81058arXiv1602.00528OpenAlexW3105496389MaRDI QIDQ2359258

Fábio G. Ribeiro, Cristiano C. Bastos, Luiz C. B. da Silva

Publication date: 28 June 2017

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

Full work available at URL: https://arxiv.org/abs/1602.00528

zbMATH Keywords

surfaces of revolutionbound statesprescribed curvaturehelicoidal surfacesconstrained dynamicsinvariant surfaces

Mathematics Subject Classification ID

Constrained dynamics, Dirac's theory of constraints (70H45) Differential geometric methods, including holonomy, Berry and Hannay phases, Aharonov-Bohm effect, etc. in quantum theory (81Q70) Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices (81Q35)

Related Items

Classification of rotational surfaces with constant skew curvature in 3-space forms, Quantization of Hamiltonian systems with a position dependent mass: Killing vector fields and Noether momenta approach, Surfing on curved surfaces -- the Maple package Surf, Exact solutions of Schrödinger and Pauli equations for a charged particle on a sphere and interacting with non-central potentials, Schrödinger formalism for a particle constrained to a surface in R13, Geometric phases for classical and quantum dynamics: Hannay angle and Berry phase for loops on a torus, Surfaces of revolution with prescribed mean and skew curvatures in Lorentz-Minkowski space

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the quantum mechanics of a particle constrained to generalized cylinders with application to Möbius strips
• Quantum motion of a point particle in the presence of the Aharonov-Bohm potential in curved space
• Generalised quantum waveguides
• Surfaces of revolution with prescribed mean curvature
• Helicoidal surfaces with constant mean curvature
• Helicoidal surfaces with prescribed mean or Gaussian curvature
• Quantum mechanics on manifolds embedded in Euclidean space.
• Quantum strips on surfaces
• On the quantum dynamics of a point particle in conical space
• Notes on the quantum mechanics of particles constrained to curved surfaces
• Nonrelativistic quantum dynamics on a cone with and without a constraining potential
• Quantum dynamics of a particle constrained to lie on a surface
• Schrödinger problems for surfaces of revolution—the finite cylinder as a test example
• Bound states in one and two spatial dimensions
• Gauge fields and extrapotentials in constrained quantum systems
• On the mathematical treatment of the Born-Oppenheimer approximation
• Dynamical Theory in Curved Spaces. I. A Review of the Classical and Quantum Action Principles
• The Monge-Ampère equation
• Realizing holonomic constraints in classical and quantum mechanics