Related papers: The kinetic energy operator in the subspaces of wa…
We define a deformed kinetic energy operator for a discrete position space with a finite number of points. The structure may be either periodic or nonperiodic with well-defined end points. It is shown that for the nonperiodic case the…
The approximate representation of operators by finite matrices is analysed in terms of accuracy and convergence. The identity operator, for example, can be reconstructed using a basis of harmonic oscillator states leading to a narrow peak…
We study 2d vortex sheets with unbounded support. First we show a version of the Biot- Savart law related to a class of objects including such vortex sheets. Next, we give a formula associating the kinetic energy of a very general class of…
The energy dissipation in a gas of structured objects, e.g. molecules, is considered in density matrix formalism. It is shown that the macroscopic irreversibility of the kinetic processes can be considered as a consequence of the…
We propose a simple density functional expression for the upper bound of the kinetic energy for electronic systems. Such a functional is valid in the limit of slowly varying density, its validity outside this regime is discussed by making a…
Incremental models for magnetic vector hysteresis have been developed in previous works in accordance with basic principles of thermodynamics. In this paper, we present an equivalent representation of the associated hysteresis operator in…
The choice of mathematical representation when describing physical systems is of great consequence, and this choice is usually determined by the properties of the problem at hand. Here we examine the little-known wave operator…
We report on the effect of the kinetic energy operator ambiguity on the energy spectra of various double heterostructures when the mass of the charge carriers, subjected to a potential, depends on position. The spectra are calculated using…
The kinetic energy operator of a quantum particle with position dependent mass and the associated ordering ambiguity is revisited. We introduce a new form of this operator which is a continues or discreet superposition of the acceptable…
An efficient numerical quadrature is proposed for the approximate calculation of the potential energy in the context of pseudo potential electronic structure calculations with Daubechies wavelet and scaling function basis sets. Our…
We present a novel route to constructing cost-efficient semi-empirical approximations for the non-additive kinetic energy in subsystem density functional theory. The developed methodology is based on the use of Slater determinants composed…
We consider two different relativistic versions of the Kepler problem in the plane: the first one involves the relativistic differential operator, the second one involves a correction for the usual gravitational potential due to…
A mathematical framework is constructed for the sum of the lowest N eigenvalues of a potential. Exactness is illustrated on several model systems (harmonic oscillator, particle in a box, and Poschl-Teller well). Its order-by-order…
A concept of kinetic energy in quantum mechanics is analyzed. Kinetic energy is a non-zero positive value in many cases of bound states, when a wave function is a real-valued one and there are no visible motion and flux. This can be…
It is shown that the well-known relativistic correction of quantum Hamiltonian that is present in textbooks appears after quantization of oversimplified relativistic kinetic energy decomposition. Using the proper expression one obtains the…
We study three well known models of matter coupled to the ultraviolet cutoff, quantized radiation field and to the Coulomb potential of arbitrarily many nuclei. Two are nonrelativistic: the first uses the kinetic energy (p+eA(x))^2 and the…
We present a method for calculating the kinetic energy of localised functions represented on a regular real space grid. This method uses fast Fourier transforms applied to restricted regions commensurate with the simulation cell and is…
We show that the central finite difference formula for the first and the second derivative of a function can be derived, in the context of quantum mechanics, as matrix elements of the momentum and kinetic energy operators using, as a basis…
A weak notion of elastic energy for (not necessarily regular) rectifiable curves in any space dimension is proposed. Our $p$-energy is defined through a relaxation process, where a suitable $p$-rotation of inscribed polygonals is adopted.…
A one-dimensional Schr\"odinger equation with position-dependent effective mass in the kinetic energy operator is studied in the framework of an $so(2,1)$ algebra. New mass-deformed versions of Scarf II, Morse and generalized…