Related papers: New Quantum System of Wilson Orthogonal Polynomial
In this article, we provide an overview of the basic concepts of novel topological materials. This new class of materials developed by combining the Weyl/Dirac fermionic electron states and magnetism, provide a materials-science platform to…
Mechanical resonators are gradually becoming available as new quantum systems. Quantum optics in combination with optomechanical interactions (quantum optomechanics) provides a particularly helpful toolbox for generating and controlling…
In analogy with conventional quantum mechanics, non-commutative quantum mechanics is formulated as a quantum system on the Hilbert space of Hilbert-Schmidt operators acting on non-commutative configuration space. It is argued that the…
A quaternionic version of Quantum Mechanics is constructed using the Schwinger's formulation based on measurements and a Variational Principle. Commutation relations and evolution equations are provided, and the results are compared with…
We propose a new formalism of quantum subsystems which allows to unify the existing and new methods of reduced description of quantum systems. The main mathematical ingredients are completely positive maps and correlation functions. In this…
The behavior of the quantum potential is studied for a particle in a linear and a harmonic potential by means of an extended phase space technique. This is done by obtaining an expression for the quantum potential in momentum space…
A novel method, connecting the space of solutions of a linear differential equation, of arbitrary order, to the space of monomials, is used for exploring the algebraic structure of the solution space. Apart from yielding new expressions for…
In this work we study the convex set of quantum states from a quantum logical point of view. We consider an algebraic structure based on the convex subsets of this set. The relationship of this algebraic structure with the lattice of…
The possibility of constructing a complete, continuous Wigner function for any quantum system has been a subject of investigation for over 50 years. A key system that has served to illustrate the difficulties of this problem has been an…
Within the frame of a novel treatment we make a complete mathematical analysis of exactly solvable one-dimensional quantum systems with non-constant mass, involving their ordering ambiguities. This work extends the results recently reported…
This thesis deals with the systematic treatment of quantum-mechanical systems in post-Newtonian gravitational fields. Starting from clearly spelled-out assumptions, employing a framework of geometric background structures defining the…
A brief description of the relations between the factorization method in quantum mechanics, self-similar potentials, integrable systems and the theory of special functions is given. New coherent states of the harmonic oscillator related to…
We define new noncommutative spheres with partial commutation relations for the coordinates. We investigate the quantum groups acting maximally on them, which yields new quantum versions of the orthogonal group: They are partially…
We consider the quantum dynamics of a test particle in noncommutative space under the influence of linearized gravitational waves in the long wave-length and low-velocity limit. A prescription for quantizing the classical Hamiltonian for…
We present a quantum algorithm based on repeated measurement to solve initial-value problems for nonlinear ordinary differential equations (ODEs), which may be generated from partial differential equations in plasma physics. We map a…
Accurate models for open quantum systems -- quantum states that have non-trivial interactions with their environment -- may aid in the advancement of a diverse array of fields, including quantum computation, informatics, and the prediction…
In this paper, we establish a $q$-integral formula by using the orthogonality relation, and also provide a new proof of the $q$-orthogonality relation for the continuous $q$-ultraspherical polynomials. A new $q$-beta integral with five…
Using a realization of the q-exponential function as an infinite multiplicative sereis of the ordinary exponential functions we obtain new nonlinear connection formulae of the q-orthogonal polynomials such as q-Hermite, q-Laguerre and…
Three sets of exactly solvable one-dimensional quantum mechanical potentials are presented. These are shape invariant potentials obtained by deforming the radial oscillator and the trigonometric/hyperbolic P\"oschl-Teller potentials in…
Some particular examples of classical and quantum systems on the lattice are solved with the help of orthogonal polynomials and its connection to continuous models are explored.