Related papers: On Potentials Integrated by the Nikiforov-Uvarov M…
Coalgebras generalize various kinds of dynamical systems occuring in mathematics and computer science. Examples of systems that can be modeled as coalgebras include automata and Markov chains. We will present a coalgebraic representation of…
The basic concepts of factorizable problems in one-dimensional Quantum Mechanics, as well as the theory of Shape Invariant potentials are reviewed. The relation of this last theory with a generalization of the classical Factorization Method…
In this work, on the condition that scalar potential is equal to vector potential, the bound state solutions of the Klein-Fock-Gordon equation of the Manning-Rosen plus ring-shaped like potential are obtained by Nikiforov-Uvarov method. The…
Density functional theory offers a very accurate way of computing materials properties from first principles. However, it is too expensive for modelling large-scale molecular systems whose properties are, in contrast, computed using…
The concept of partnership of potentials is studied in detail and in particular the non-uniqueness due to the ambiguity in the election of the factorization energy and in the choice of the solution of certain Riccati equation. We generate…
A generalized formulation of non-relativistic quantum mechanics is developed within multidimensional geometric (NG) frameworks characterized by a power-law dispersion relation \(E \propto |p|^{j}\), where \(j = N - 1\). Starting from the…
Quantum computers take advantage of interfering quantum alternatives in order to handle problems that might be too time consuming with algorithms based on classical logic. Developing quantum computers requires new ways of thinking beyond…
Quantum nonrelativistic systems with $2\times2$ matrix potentials are investigated. Physically, they simulate charged or neutral fermions with non-trivial dipole momenta, interacting with an external electric field. Assuming rotationally…
Large-scale atomistic computer simulations of materials rely on interatomic potentials providing computationally efficient predictions of energy and Newtonian forces. Traditional potentials have served in this capacity for over three…
Based on ideas of quantum theory of open systems we propose the consistent approach to the formulation of logic of plausible propositions. To this end we associate with every plausible proposition diagonal matrix of its likelihood and…
We propose a novel method to describe realistically ionization processes with absorbing boundary conditions in basis expansion within the formalism of the so-called Non-Adiabatic Quantum Molecular Dynamics. This theory couples…
We consider the quantum simulation of relativistic quantum mechanics, as described by the Dirac equation and classical potentials, in trapped-ion systems. We concentrate on three problems of growing complexity. First, we study the…
We extend the notion of Dirac oscillator in two dimensions, to construct a set of potentials. These potentials becomes exactly and quasi-exactly solvable potentials of non-relativistic quantum mechanics when they are transformed into a…
Quantum Mechanics is a good example of a successful theory. Most of atomic phenomena are described well by quantum mechanics and cases such as Lamb Shift that are not described by quantum mechanics, are described by quantum electrodynamics.…
We consider a superintegrable quantum potential in two-dimensional Euclidean space with a second and a third order integral of motion. The potential is written in terms of the fourth Painleve transcendent. We construct for this system a…
We develop an algebraic frame for the simultaneous treatment of actual and possible properties of quantum systems. We show that, in spite of the fact that the language is enriched with the addition of a modal operator to the orthomodular…
After an historical introduction on the standard algebraic approach to quantum mechanics of large systems we review the basic mathematical aspects of the algebras of unbounded operators. After that we discuss in some details their relevance…
Solvable Natanzon potentials in nonrelativistic quantum mechanics are known to group into two disjoint classes depending on whether the Schr\"odinger equation can be reduced to a hypergeometric or a confluent hypergeometric equation. All…
A quantum measurement model based upon restricted path-integrals allows us to study measurements of generalized position in various one-dimensional systems of phenomenological interest. After a general overview of the method we discuss the…
We are dealing in this work with such formal and conceptual extensions of nonrelativistic quantum mechanics (QM) which contain QM with its standard formalism and interpretation as a subtheory. QM is here primarily equivalently reformulated…