Related papers: Applying Classical Geometry Intuition to Quantum S…
The Hamiltonian conservative system of two interacting particles has been considered both in classical and quantum description. The quantum model has been realized using a symmetrized two-particle basis reordered in the unperturbed energy.…
An analysis is made within the quantum formalism of the probabilistic features of the electron spin correlation, with the purpose of clarifying the concepts of contextuality and measurement dependence. The quantum formulas for the spin…
In physical experiments, reference frames are standardly modelled through a specific choice of coordinates used to describe the physical systems, but they themselves are not considered as such. However, any reference frame is a physical…
Analytical expressions are derived for sums of matrix elements and their squared moduli over many-body states with given total spin --- the states built from spin and spatial wavefunctions belonging to multidimensional irreducible…
In this paper, the principles of the general relativity are used to formulate quantum wave equations for spin-0 and spin-1/2 particles. More specifically, the equations are worked in a Schwarzschild-like metric. As a test, the hydrogen atom…
Coherent states, and the Hilbert space representations they generate, provide ideal tools to discuss classical/quantum relationships. In this paper we analyze three separate classical/quantum problems using coherent states, and show that…
The aim of the paper is to extend the notion of $\alpha$-geometry in the classical and in the noncommutative case by introducing a more general class of pull-back metrics and to give concrete formulas for the scalar curvature of these…
We investigate a quantum nonrelativistic system describing the interaction of two particles with spin 1/2 and spin 0, respectively. We assume that the Hamiltonian is rotationally invariant and parity conserving and identify all such systems…
A number of recent proposals for a quantum theory of gravity are based on the idea that spacetime geometry and gravity are derivative concepts and only apply at an approximate level. There are two fundamental challenges to any such…
With the growth of geometric science, including the methods of exploring the world of information by means of modern geometry, there has always been a mysterious and fascinating ambiguous link between geometric, topological and dynamical…
The present monograph explores the correspondence between quantum and classical mechanics in the particular context of spin systems, that is, SU(2)-symmetric mechanical systems. Here, a detailed presentation of quantum spin-j systems, with…
We investigate the phase structure of three-dimensional quantum gravity coupled to an Ising spin system by means of numerical simulations. The quantum gravity part is modelled by the summation over random simplicial manifolds, and the Ising…
Observables in a quantum system, represented by a Hilbert space, are given by the orthogonal bases of the aforementioned Hilbert space. Categorical Quantum Mechanics provides further abstraction of such observables, allowing for a…
Quantum mechanics increasingly penetrates modern technologies but, due to its non-deterministic nature seemingly contradicting our classical everyday world, our comprehension often stays elusive. Arguing along the correspondence principle,…
Symmetry adapted bases in quantum chemistry and bases adapted to quantum information share a common characteristics: both of them are constructed from subspaces of the representation space of the group SO(3) or its double group (i.e.,…
A comparative analysis of the Mathisson-Papapetrou and Pomeransky-Khriplovich equations is presented. Motion of spinning particles and their spins in gravitational fields and noninertial frames is considered. The angular velocity of spin…
Quantum mechanics is among the most important and successful mathematical model for describing our physical reality. The traditional formulation of quantum mechanics is linear and algebraic. In contrast classical mechanics is a geometrical…
The classical invariants of a Hamiltonian system are expected to be derivable from the respective quantum spectrum. In fact, semiclassical expressions relate periodic orbits with eigenfunctions and eigenenergies of classical chaotic…
Classical mechanics is formulated in complex Hilbert space with the introduction of a commutative product of operators, an antisymmetric bracket, and a quasidensity operator. These are analogues of the star product, the Moyal bracket, and…
All existing experimental results are currently interpreted using classical geometry. However, there are theoretical reasons to suspect that at a deeper level, geometry emerges as an approximate macroscopic behavior of a quantum system at…