相关论文: The Canonical Function Method and its applications…

The problem of defining and constructing representations of the Canonical Commutation Relations can be systematically approached via the technique of {\it algebraic quantization}. In particular, when the phase space of the system is linear…

The representation of a Schrodinger equations as a classic Hamiltonian system allows to construct a unified perturbation theory both in classic, and in a quantum mechanics grounded on the theory of canonical transformations, and also to…

This note carries three purposes involving our latest advances on the radial basis function (RBF) approach. First, we will introduce a new scheme employing the boundary knot method (BKM) to nonlinear convection-diffusion problem. It is…

A new formulation of potential scattering in quantum mechanics is developed using a close structural analogy between partial waves and the classical dynamics of many non-interacting fields. Using a canonical formalism we find non-linear…

A new mathematical model for the description of three electron quantum dots in 2D space is created, and ground states of this system in external magnetic field is investigated. The Schrodinger equation for three two-dimensional electrons is…

Fradkin's representation is a general method of attacking problems in quantum field theory, having as its basis the functional approach of Schwinger. As a pedagogical illustration of that method, we explicitly formulate it for quantum…

A careful functional treatment of quantum scattering is given using Schwinger's dynamical principle which involves a functional differentiation operation applied to a generating functional written in closed form. For long range…

We show that it is possible to obtain numerical solutions to quantum mechanical problems involving a fractional Laplacian, using a collocation approach based on Little Sinc Functions (LSF), which discretizes the Schr\"odinger equation on a…

Quantum computing is a promising new area of computing with quantum algorithms offering a potential speedup over classical algorithms if fault tolerant quantum computers can be built. One of the first applications of the classical computer…

It is argued that, contrary to conventional wisdom, no trustworthy universal self-force/radiative corrections to the Lorentz force equation, can be derived from the basic tenets of classical electrodynamics. This concords with the apparent…

Scattered data fitting is a frequently encountered problem for reconstructing an unknown function from given scattered data. Radial basis function (RBF) methods have proven to be highly useful to deal with this problem. We describe two…

Quantum mechanics/molecular mechanics (QM/MM) is a standard computational tool for describing chemical reactivity in systems with many degrees of freedom, including polymers, enzymes, and reacting molecules in complex solvents. However,…

The Wave Function Matching (WFM) technique has recently been developed for the calculation of electronic transport in quantum two-probe systems. In terms of efficiency it is comparable with the widely used Green's function approach. The WFM…

The present paper engages in a particular attempt to acquire exact analytical eigensolutions of the position-dependent effective mass (PDEM) Schr\"odinger equation for a variety of squared style trigonometric potentials. The algebraic…

Canonical quantization of the photon -- a free massless vector field -- is considered in cosmological spacetimes in a two-parameter family of linear gauges that treat all the vector potential components on equal footing. The goal is setting…

The method of differential equations has been proven to be a powerful tool for the computation of multi-loop Feynman integrals appearing in quantum field theory. It has been observed that in many instances a canonical basis can be chosen,…

The method of fundamental solutions (MFS) is a numerical method for solving boundary value problems involving linear partial differential equations. It is well known that it can be very effective assuming regularity of the domain and…

We propose a method for preparing the quantum state for a given velocity field, e.g., in fluid dynamics, via the spherical Clebsch wave function (SCWF). Using the pointwise normalization constraint for the SCWF, we develop a variational…

Quantum Monte Carlo (QMC) methods represent a powerful family of computational techniques for tackling complex quantum many-body problems and performing calculations of stationary state properties. QMC is among the most accurate and…

Time-dependent quantum mechanics provides an intuitive picture of particle propagation in external fields. Semiclassical methods link the classical trajectories of particles with their quantum mechanical propagation. Many analytical results…