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We provide a representation of the $C^*$-algebra generated by multidimensional integral operators with piecewise constant kernels and discrete ergodic operators. This representation allows us to find the spectrum and to construct the…
Quantum algorithms are able to solve particular problems exponentially faster than conventional algorithms, when implemented on a quantum computer. However, all demonstrations to date have required already knowing the answer to construct…
In this paper, we discuss index theory for Toeplitz operators on a discrete quarter-plane of two-variable rational matrix function symbols. By using Gohberg-Krein theory for matrix factorizations, we extend the symbols defined originally on…
We study some classes of symmetric operators for the discrete series representations of the quantum algebra U_q(su_{1,1}), which may serve as Hamiltonians of various physical systems. The problem of diagonalization of these operators…
The Laplace-Beltrami problem on closed surfaces embedded in three dimensions arises in many areas of physics, including molecular dynamics (surface diffusion), electromagnetics (harmonic vector fields), and fluid dynamics (vesicle…
Quantum computers can be used to address molecular structure, materials science and condensed matter physics problems, which currently stretch the limits of existing high-performance computing resources. Finding exact numerical solutions to…
Green-hyperbolic operators - partial differential operators on globally hyperbolic spacetimes that (together with their formal duals) possess advanced and retarded Green operators - play an important role in many areas of mathematical…
The correspondence between the integrability of classical mechanical systems and their quantum counterparts is not a 1-1, although some close correspondencies exist. If a classical mechanical system is integrable with invariants that are…
In this paper, we study within the structure of Symplectic Quantum Mechanics a bi-dimensional non-relativistic strong interaction system which represent the bound state of heavy quark-antiquark, where we consider a Cornell potential which…
Using algebraic tools of supersymmetric quantum mechanics we construct classes of conditionally exactly solvable potentials being the supersymmetric partners of the linear or radial harmonic oscillator. With the help of the raising and…
Implementing general functions of operators is a powerful tool in quantum computation. It can be used as the basis for a variety of quantum algorithms including matrix inversion, real and imaginary-time evolution, and matrix powers. Quantum…
Morse oscillator is one of the known solvable potentials which attracts many applications in quantum mechanics especially in quantum chemistry. One of the interesting results of this study is the generation of ladder operators for Morse…
In 1968, Gohberg and Krupnik found a Fredholm criterion for singular integral operators of the form $aP+bQ$, where $a,b$ are piecewise continuous functions and $P,Q$ are complementary projections associated to the Cauchy singular integral…
A unitary operator which relates the system of a particle in a linear potential with time-dependent parameters to that of a free particle, has been given. This operator, closely related to the one which is responsible for the existence of…
A time fractional quantum framework has been introduced into quantum mechanics. A new version of the space-time fractional Schr\"odinger equation has been launched. The introduced space-time fractional Schr\"odinger equation has a new scale…
We address the problem of integrating operator equations concomitant with the dynamics of non autonomous quantum systems by taking advantage of the use of time-dependent canonical transformations. In particular, we proceed to a discussion…
Relations between Hamiltonian mechanics and quantum mechanics are studied. It is stressed that classical mechanics possesses all the specific features of quantum theory: operators, complex variables, probabilities (in case of ergodic…
Problems of the numerical solution of the Cauchy problem for a first-order differential-operator equation are discussed. A fundamental feature of the problem under study is that the equation includes a fractional power of the self-adjoint…
Our previous work on the one-dimensional KPZ equation with sharp wedge initial data is extended to the case of the joint height statistics at n spatial points for some common fixed time. Assuming a particular factorization, we compute an…
A linear quantum harmonic oscillator factors into one dimensional oscillators and can be solved using creation and annihilation operators. We consider a spherical analogue. This analogue does not factor. The two dimensional case is…