Quantum mechanics of a constrained particle and the problem of prescribed geometry-induced potential
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Publication:2359258
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
surfaces of revolutionbound statesprescribed curvaturehelicoidal surfacesconstrained dynamicsinvariant surfaces
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)
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Cites Work
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- 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