Related papers: The Rayleigh Quotient
The main aim of this paper is to find the estimation for Vilenkin-Fourier coefficients.
Program review in the physical sciences may benefit from a framework within which to quantitatively discuss the scientific merit of a proposed theoretical program of research, and to assess the scientific merit of a particular theoretical…
The quantum mechanics description of a physical object stretched in space and stable in time from the relativistic space-time properties point of view, introduced in special theory of relativity, is considered and analysed. The mathematical…
It is often assumed that few- and many-body systems can be accurately described by considering only pairwise two-body interactions of the constituents. We illustrate that three- and higher-body forces enter naturally in effective field…
Learning to use math in science is a non-trivial task. It involves many different skills (not usually taught in a math class) that help blend physical knowledge with mathematical symbology. One of these is the idea of quantification: that…
The quantum version of the free fall problem is a topic often skipped in undergraduate quantum mechanics courses because its discussion usually requires wavepackets built on the Airy functions -- a difficult computation. Here, on the…
The mean field theory, in its different hues, form one of the most useful tools for calculating the single-body physical properties of a many-body system. It provides important information, like critical exponents, of the systems that do…
The classical limit of quantum mechanics is investigated, by focusing on the study of the center of mass of a many-body system where each particle is described by quantum mechanics. We study how, in the limit when the number of particles…
In this article we study the estimation of bifurcation coefficients in nonlinear branching problems by means of Rayleigh-Ritz approximation to the eigenvectors of the corresponding linearized problem. It is essential that the approximations…
A large collaboration carefully benchmarks 20 first principles many-body electronic structure methods on a test set of 7 transition metal atoms, and their ions and monoxides. Good agreement is attained between the 3 systematically converged…
The sample correlation coefficient $R$ plays an important role in many statistical analyses. We study the moments of $R$ under the bivariate Gaussian model assumption, provide a novel approximation for its finite sample mean and connect it…
In this paper we consider the central force problem in the special theory of relativity. We derive the special relativistic version of the Binet equation describing the orbit of a body. Then, the motion of a planet in a solar-like system…
The thermal or equilibrium ensemble is one of the most ubiquitous states of matter. For models comprised of many locally interacting quantum particles, it describes a wide range of physical situations, relevant to condensed matter physics,…
The blackbody is considered in the external general field. The additional coefficients of stimulated emission and absorption are introduced into the Einstein mechanism. Then, the generalized Planck formula is derived. The Einstein and Debye…
We study the rational approximation properties of special manifolds defined by a set of polynomials with rational coefficients. Mostly we will assume the case of all polynomials to depend on only one variable. In this case the manifold can…
Determining the power distribution of the members of a shareholder meeting or a legislative committee is a well-known problem for many applications. In some cases it turns out that power is nearly proportional to relative voting weights,…
These notes offer a basic introduction to the primary mathematical concepts of quantum physics, and their physical significance, from the operator and Hilbert space point of view, highlighting more what are essentially the abstract…
In this thesis we present new results relevant to two important problems in quantum information science: the development of a theory of entanglement and the exploration of the use of controlled quantum systems to the simulation of quantum…
A number of issues related to measurement show that self-consistency is lacking in quantum mechanics as this theory has been generally understood. Each issue is presented as a point in this paper. Each point can be resolved by incorporating…
We review a little-known treatment of the relativistic two-body bound-state problem - that provided by Two-Body Dirac Equations obtained from constraint dynamics. We describe some of its more important results, its relation to older…