Related papers: On Potentials Integrated by the Nikiforov-Uvarov M…
We propose two generalisations of the Coulomb potential equation of quantum mechanics and investigate the occurence of algebraic eigenfunctions for the corresponding Scrh\"odinger equations. Some relativistic counterparts of these problems…
A Euclidean formulation of relativistic quantum mechanics for systems of a finite number of degrees of freedom is discussed. Relativistic treatments of quantum theory are needed to study hadronic systems at sub-hadronic distance scales.…
The aim of this review is to present the list of by now a significant collection of quantum integrable models, ultralocal as well as nonultralocal, in a systematic way stressing on their underlying unifying algebraic structures. We restrict…
Recent works have independently suggested that Quantum Mechanics might permit for procedures that transcend the power of Turing Machines as well as of `standard' Quantum Computers. These approaches rely on and indicate that Quantum…
The solutions of trigonometric Scarf potential, PT/non-PT-symmetric and non-Hermitian q-deformed hyperbolic Scarf and Manning-Rosen potentials are obtained by solving the Schrodinger equation. The Nikiforov-Uvarov method is used to obtain…
In recent years, many new developments in theoretical physics, and in practical applications rely on different techniques of noncommutative algebras. In this review, we introduce the basic concepts and techniques of noncommutative physics…
The exact bound state spectrum of rationally extended shape invariant real as well as $PT$ symmetric complex potentials are obtained by using potential group approach. The generators of the potential groups are modified by introducing a new…
Algorithmic approach is based on the assumption that any quantum evolution of many particle system can be simulated on a classical computer with the polynomial time and memory cost. Algorithms play the central role here but not the…
Nuclear magnetic resonance techniques are used to realize a quantum algorithm experimentally. The algorithm allows a simple NMR quantum computer to determine global properties of an unknown function requiring fewer function ``calls'' than…
Dynamic equations of non-relativistic mechanics are written in covariant-coordinate form in terms of relative velocities and accelerations with respect to an arbitrary reference frame. The notions of the non-relativistic reference frame,…
The operator and the functional formulations of the dynamics of constrained systems are explored for determining unambiguously the quantum Hamiltonian of a nonrelativistic particle in a curved space.
Physical processes in the quantum regime possess non-classical properties of quantum mechanics. However, methods for quantitatively identifying such processes are still lacking. Accordingly, in this study, we develop a framework for…
Non-Archimedean mathematics is an approach based on fields which contain infinitesimal and infinite elements. Within this approach, we construct a space of a particular class of generalized functions, ultrafunctions. The space of…
The classical and quantum features of Nambu mechanics are analyzed and fundamental issues are resolved. The classical theory is reviewed and developed utilizing varied examples. The quantum theory is discussed in a parallel presentation,…
We propose a general method for introducing extensive characteristics of quantum entanglement. The method relies on polynomials of nilpotent raising operators that create entangled states acting on a reference vacuum state. By introducing…
The first of the two related papers analising and explaining the origin, manifestations and parodoxical features of the quantum potential (QP) from the non-relativistic and relativistic point of view. QP arises in the quantum Hamiltonian,…
The essence of the path integral method in quantum physics can be expressed in terms of two relations between unitary propagators, describing perturbations of the underlying system. They inherit the causal structure of the theory and its…
This document is meant as a pedagogical introduction to the modern language used to talk about quantum theory, especially in the field of quantum information. It assumes that the reader has taken a first traditional course on quantum…
A system of interacting atoms is represented as an union of two subsystems, one of which is the system of atoms, and the other is an auxiliary scalar covariant field, which is equivalent to a given static interatomic potential of general…
Relativistic invariance in Euclidean formulations of quantum mechanics is discussed. Relativistic treatments of quantum theory are needed to study hadronic systems at sub-hadronic distance scales. Euclidean formulations of relativistic…