相关论文: Integrable and superintegrable quantum systems in …

The geometric approach to mechanics based on the Jacobi metric allows to easily construct natural mechanical systems which are integrable (actually separable) at a fixed value of the energy. The aim of the present paper is to investigate…

Resonant systems emerge as weakly nonlinear approximations to problems with highly resonant linearized perturbations. Examples include nonlinear Schroedinger equations in harmonic potentials and nonlinear dynamics in Anti-de Sitter…

In absence of currents and charges the quantized electromagnetic field can be described by wave functions which for each individual wave vector are normalized to one. The resulting formalism involves reducible representations of the…

The superposition of the Kepler-Coulomb potential on the 3D Euclidean space with three centrifugal terms has recently been shown to be maximally superintegrable [Verrier P E and Evans N W 2008 J. Math. Phys. 49 022902] by finding an…

We consider some examples of quantum super-integrable systems and the associated nonlinear extensions of Lie algebras. The intimate relationship between super-integrability and exact solvability is illustrated. Eigenfunctions are…

A classical (or quantum) second order superintegrable system is an integrable n-dimensional Hamiltonian system with potential that admits 2n-1 functionally independent second order constants of the motion polynomial in the momenta, the…

In this contribution, we discuss three situations in which complete integrability of a three dimensional classical system and its quantum version can be achieved under some conditions. The former is a system with axial symmetry. In the…

We consider an open domain with a compact boundary in an Euclidean space and a Schroedinger operator with magnetic field on this domain. We give sufficient conditions on the rate of growth of the magnetic field near the boundary which…

The wide-spread opinion is that original quantum mechanics is a reversible theory, but this statement is only true for undecomposed systems, that are those systems which sub-systems are out of consideration. Taking sub-systems into account,…

The N-dimensional generalization of Bertrand spaces as families of Maximally superintegrable systems on spaces with nonconstant curvature is analyzed. Considering the classification of two dimensional radial systems admitting 3 constants of…

We consider a relativistic charged particle in background electromagnetic fields depending on both space and time. We identify which symmetries of the fields automatically generate integrals (conserved quantities) of the charge motion,…

It is argued that the dynamics of an isolated system, due to the concrete procedure by which it is separated from the environment, has a non-Hamiltonian contribution. By a unified quantum field theoretical treatment of typical subdynamics,…

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…

The quantum dynamics of an electron in a uniform magnetic field is studied for geometries corresponding to integrable cases. We obtain the uniform asymptotic approximation of the WKB energies and wavefunctions for the semi-infinite plane…

We show how quantum mechanics can be understood as a space-time theory provided that its spatial continuum is modelled by a variable real number (qrumber) continuum. Such a continuum can be constructed using only standard Hilbert space…

We formulate quantum mechanics in spacetimes with real-order fractional geometry and more general factorizable measures. In spacetimes where coordinates and momenta span the whole real line, Heisenberg's principle is proven and the…

Quantum mechanics is widely regarded as a complete theory, yet we argue it is a tractable projection of a deeper, computationally-inaccessible classical variational structure. By analyzing the coupled partial differential equations of the…

In this paper we give examples of applications of general methods of quantization by symmetrization of classical integrable systems, which have been illustrated in two previous works by the same authors. We consider two classes of systems…

We review some known results on the superintegrability of monopole systems in the three-dimensional (3D) Euclidean space and in the 3D generalized Taub-NUT spaces. We show that these results can be extended to certain curved backgrounds…

At present, our notion of space is a classical concept. Taking the point of view that quantum theory is more fundamental than classical physics, and that space should be given a purely quantum definition, we revisit the notion of Euclidean…