Related papers: Locally curved quantum layers
We consider a nonrelativistic quantum particle constrained to a curved layer of constant width built over a non-compact surface embedded in $R^3$. We suppose that the latter is endowed with the geodesic polar coordinates and that the layer…
It has been shown recently that a nonrelativistic quantum particle constrained to a hard-wall layer of constant width built over a geodesically complete simply connected noncompact curved surface can have bound states provided the surface…
Combination of a construction of unambiguous quantum conditions out of the conventional one and a simultaneous quantization of the positions, momenta, angular momenta and Hamiltonian leads to the geometric potential given by the so-called…
Consider a quantum particle trapped between a curved layer of constant width built over a complete, non-compact, $\mathcal C^2$ smooth surface embedded in $\mathbb{R}^3$. We assume that the surface is asymptotically flat in the sense that…
We study spectral and scattering properties of a spinless quantum particle confined to an infinite planar layer with hard walls containing a finite number of point perturbations. A solvable character of the model follows from the explicit…
We investigate the effect of curvature on the behaviour of a quantum particle bound to move on a surface. For the Gaussian bump we derive and discuss the quantum potential which results in the appearance of a bound state for particles with…
We clearly refine the fundamental framework of the thin-layer quantization procedure, and further develop the procedure by taking the proper terms of degree one in $q_3$ ($q_3$ denotes the curvilinear coordinate variable perpendicular to…
Motivated by the theory of quantum waveguides, we investigate the spectrum of the Laplacian, subject to Dirichlet boundary conditions, in a curved strip of constant width that is defined as a tubular neighbourhood of an infinite curve in a…
In this paper, we study the bound states of quantum layers. We prove that for the quantum layer built over a parabolic manifold which is not totally geodesic, if the second fundamantal form decays sufficiently fast, then the bound states…
The Schrodinger equation for a charged particle constrained to a curved surface in the presence of a vector potential is derived using the method of forms. In the limit that the particle is brought infinitesimally close to the surface, a…
We analyze constrained quantum systems where the dynamics do not preserve the constraints. This is done in particular for the restriction of a quantum particle in Euclidean n-space to a curved submanifold, and we propose a method of…
The motion of quantum particles homogeneously constrained to a curved surface is affected by a curvature induced geometric potential. Here, we consider the case of inhomogeneous confinement and derive the effective Hamiltonian by extending…
We derive an effective Hamiltonian for a quantum system constrained to a submanifold (the constraint manifold) of configuration space (the ambient space) by an infinite restoring force. We pay special attention to how this Hamiltonian…
We derive the Schroedinger equation for a spinless charged particle constrained to a curved surface with electric and magnetics fields applied. The particle is confined on the surface using a thin-layer procedure, giving rise to the…
We consider one particle confined to a deformed one-dimensional wire. The quantum mechanical equivalent of the classical problem is not uniquely defined. We describe several possible hamiltonians and corresponding solutions for a finite…
Quantum particles confined to surfaces in higher dimensional spaces are acted upon by forces that exist only as a result of the surface geometry and the quantum mechanical nature of the system. The dynamics are particularly rich when…
We investigate the controllability of an infinite-dimensional quantum system: a quantum particle confined on a Thick Quantum Graph, a generalisation of Quantum Graphs whose edges are allowed to be manifolds of arbitrary dimension with…
We consider the quantum dynamics of a charged particle in Euclidean space subjected to electric and magnetic fields under the presence of a potential that forces the particle to stay close to a compact surface. We prove that, as the…
The quantization of a single particle without spin in an appropriate curved space-time is considered. The Hamilton formalism on reduced space for a particle in a curved space-time is constructed and the main aspects of quantization scheme…
We show that quantum particles constrained to move along curves undergoing cyclic deformations acquire, in general, geometric phases. We treat explicitly an example, involving particular deformations of a circle, and ponder on potential…