相关论文: Algebraic Representation of Many-Particle Coulomb …

We study the Hydrogen atom as a quantum mechanical system with a Coulomb like potential, with a semiclassical approach based on an effective description of quantum mechanics. This treatment allows us to describe the quantum state of the…

Quantum physics has revealed many interesting formal properties associated with the algebra of two operators, A and B, satisfying the partial commutation relation AB-BA=1. This study surveys the relationships between classical combinatorial…

The calculation time for the energy of atoms and molecules scales exponentially with system size on a classical computer but polynomially using quantum algorithms. We demonstrate that such algorithms can be applied to problems of chemical…

We study a physically motivated representation of an algebra of operators in gravitational and non gravitational theories called the covariant representation of an algebra. This is a representation where the symmetries of the operator…

We develop a new algebraic setting for treating piecewise functions and distributions together with suitable differential and Rota-Baxter structures. Our treatment aims to provide the algebraic underpinning for symbolic computation systems…

Green's function theory has emerged as a powerful many-body approach not only in condensed matter physics but also in quantum chemistry in recent years. We have developed a new all-electron implementation of the BSE@GW formalism using…

We introduce the Green's functions technique as an alternative theory to the quantum regression theorem formalism for calculating the two-time correlation functions in open quantum systems. In particular, we investigate the potential of…

New algebraic approach to analytical calculations of D-dimensional integrals for multi-loop Feynman diagrams is proposed. We show that the known analytical methods of evaluation of multi-loop Feynman integrals, such as integration by parts…

We consider relationships between cubic algebras and implication algebras. We first exhibit a functorial construction of a cubic algebra from an implication algebra. Then we consider an collapse of a cubic algebra to an implication algebra…

We present a family of algorithms for the numerical approximation of the Schr\"odinger equation with potential concentrated at a finite set of points. Our methods belong to the so-called fast and oblivious convolution quadrature algorithms.…

We present a detailed study of the representations of the algebra of functions on the quantum group $ GL_q(n) $. A q-analouge of the root system is constructed for this algebra which is then used to determine explicit matrix representations…

We consider the two-dimensional non-relativistic Coulomb problem with the aid of the momentum space construction of the associated Green's function. Our presentation has precursors in three dimensions. It is mainly Schwinger's approach…

Exact calculation of electronic properties of molecules is a fundamental step for intelligent and rational compounds and materials design. The intrinsically graph-like and non-vectorial nature of molecular data generates a unique and…

An explicit solution for the generating functional of n-point functions in the planar approximation is given in terms of two sets of free-algebraic annihilation and creation operators.

A explicit formula on semiclassical Green functions in mixed position and momentum spaces is given, which is based on Maslov's multi-dimensional semiclassical theory. The general formula includes both coordinate and momentum representations…

The Laguerre functions constitute one of the fundamental basis sets for calculations in atomic and molecular electron-structure theory, with applications in hadronic and nuclear theory as well. While similar in form to the Coulomb…

A new density matrix and corresponding quantum kinetic equations are introduced for fermions undergoing coherent evolution either in time (coherent particle production) or in space (quantum reflection). A central element in our derivation…

Some properties of the fractional Fourier transform, which is used in information processing, are presented in connection with the tomography transform of optical signals. Relation of the Green function of the quantum harmonic oscillator to…

We investigate symmetric oscillators, and in particular their quantization, by employing semiclassical and quantum phase functions introduced in the context of Liouville-Green transformations of the Schr\"{o}dinger equation. For anharmonic…

We provide explicit representations of Green's functions for general linear fractional differential operators with {\it variable coefficients} and Riemann-Liouvilles derivatives. We assume that all their coefficients are continuous in $[0,…