Related papers: On relation between geometric momentum and annihil…
There has been an extended debate regarding the existence of a spin-orbital decomposition of the angular momentum of photons and other massless particles. It was recently shown that there are both geometric and topological obstructions…
The geometric structure of quantum states plays a fundamental role in determining the intrinsic dynamics of electrons in solids. In this work, we study the geometric origin of orbital angular momentum and its transport in a general two-band…
We perform quantization of a model in which gravity is coupled to a circular dust shell in 2+1 spacetime dimensions. Canonical analysis shows that momentum space of this model is ADS^2-space, and the global chart for it is provided by the…
In a (1+1)-dimensional midi-superspace model for gravitational plane waves, a flat space-time condition is imposed with constraints derived from null Killing vectors. Solutions to a straightforward regularization of these constraints have…
Physical mechanism for the geometric phase in terms of angular momentum exchange is elucidated. It is argued that the geometric phase arising out of the cyclic changes in the tranverse mode space of the Gaussian light beams is a…
The aim of Part II of this paper is to try to describe wave functions on q-deformed versions of position and momentum space. This task is done within the framework developed in Part I of the paper. In order to make Part II self-contained…
It is shown that the 2 X 2 matrix Hamiltonian describing the dynamics of a charged spin 1/2 particle with g-factor 2 moving in an arbitrary, spatially dependent, magnetic field in two spatial dimensions can be written as the anticommuator…
Finite-dimensional Quantum Mechanics can be geometrically formulated as a proper classical-like Hamiltonian theory in a projective Hilbert space. The description of composite quantum systems within the geometric Hamiltonian framework is…
The quantum mechanical formalism for position and momentum of a particle in a one dimensional cyclic lattice is constructively developed. Some mathematical features characteristic of the finite dimensional Hilbert space are compared with…
Based on the recent construction of a self-adjoint momentum operator for a particle confined in a one-dimensional interval, we extend the construction to arbitrarily shaped regions in any number of dimensions. Different components of the…
We analyze the position and momentum uncertainties of the energy eigenstates of the harmonic oscillator in the context of a deformed quantum mechanics, namely, that in which the commutator between the position and momentum operators is…
The momentum operator for a spin-less particle when confined to a 2D surface embedded into 3D space acquires a geometrical component proportional to the mean curvature that renders it Hermitian. As a consequence, the quantum force operator…
In the spirit of the thin-layer quantization approach, we give the formula of the geometric influences of a particle confined to a curved surface embedded in three-dimensional Euclidean space. The geometric contributions can result from the…
The monitoring of the three independent components of the angular momentum (or spin) of a quantum system by its environment that does not isolate any preferred orientation is modelled in two different ways. One describes the dynamics by the…
This paper claims that local space-time curvature can non-trivially contribute to the properties of orbital angular momentum in quantum mechanics. Of key importance is the demonstration that an extended orbital angular momentum operator due…
Using the formalism of Maya diagrams and ladder operators, we describe the algebra of annihilating operators for the class of rational extensions of the harmonic oscillator. This allows us to construct the corresponding coherent state in…
We bring the concept that quantum symmetries describe theories with nontrivial momentum space properties one step further, looking at quantum symmetries of spacetime in presence of a nonvanishing cosmological constant $\Lambda$. In…
The manifold of pure quantum states is a complex projective space endowed with the unitary-invariant geometry of Fubini and Study. According to the principles of geometric quantum mechanics, the detailed physical characteristics of a given…
The coherent states for a set of quadratic Hamiltonians in the trap regime are constructed. A matrix technique which allows to identify directly the creation and annihilation operators will be presented. Then, the coherent states as…
Complex and spinorial techniques of general relativity are used to determine all the states of the $SU(2)$ invariant quantum mechanical systems in which the equality holds in the uncertainty relations for the components of the angular…