Related papers: The two-dimensional hydrogen atom in The momentum …
The Legendre transform (LET) is a product of a general duality principle: any smooth curve is, on the one hand, a locus of pairs, which satisfy the given equation and, on the other hand, an envelope of a family of its tangent lines. An…
We use the idea of the symmetry between the spacetime coordinates x^\mu and the energy-momentum p^\mu in quantum theory to construct a momentum space quantum gravity geometry with a metric s_{\mu\nu} and a curvature P^\lambda_{\mu\nu\rho}.…
The quadrupole moment of a hydrogen atom in a magnetic field for field strengths from 0 to 4.414e13 G is calculated by two different methods. The first method is variational, and based on a single trial function. The second method deals…
Integral transforms are invaluable mathematical tools to map functions into spaces where they are easier to characterize. We introduce the hyperdimensional transform as a new kind of integral transform. It converts square-integrable…
For a hydrogen atom subject to a constant magnetic field, we report a numerical realization of the two-dimensional Non-Linearization Procedure (NLP) to estimate the accuracy of the variational energy associated with a given trial function.…
The position and momentum probability densities of a multidimensional quantum system are fully characterized by means of the radial expectation values $\langle r^\alpha \rangle$ and $\left\langle p^\alpha \right\rangle$, respectively. These…
Highly accurate nonrelativistic ground-state wave function and energy of the lithium atom is obtained in the Hylleraas basis set. The leading relativistic corrections,as represented by Breit-Pauli Hamiltonian, are obtained in fair agreement…
We study higher moments of convolutions of the characteristic function of a set, which generalize a classical notion of the additive energy. Such quantities appear in many problems of additive combinatorics as well as in number theory. In…
In this article we develop in detail a causal model of the hydrogen atom, building on the earlier work of Dewdney and Malik [1] in which they outlined a causal model of the hydrogen atom, focusing more on a causal model of angular momentum…
A simple approach for understanding the quantum nature of angular momentum and its reduction to the classical limit is presented based on Schwinger's coupled-boson representation. This approach leads to a straightforward explanation of why…
We give a numerical approximation of the L\'evy constant on the growth of the denominators of the best Diophantine approximations in dimension 2 with respect to the euclidean norm. This constant is expressed as an integral on a surface of…
We study thermodynamic properties and the electrical conductivity of dense hydrogen and deuterium using three methods: classical reactive Monte Carlo (REMC), direct path integral Monte Carlo (PIMC) and a quantum dynamics method in the…
We observe that the Schrodinger equation may be written as two real coupled Hamilton-Jacobi (HJ)-like equations, each involving a quantum potential. Developing our established programme of representing the quantum state through exact…
Momentum-space derivatives of matrix elements can be related to their coordinate-space moments through the Fourier transform. We derive these expressions as a function of momentum transfer $Q^2$ for asymptotic in/out states consisting of a…
We review the Fourier-Laguerre transform, an alternative harmonic analysis on the three-dimensional ball to the usual Fourier-Bessel transform. The Fourier-Laguerre transform exhibits an exact quadrature rule and thus leads to a sampling…
We investigate far-field radiation of energy, linear momentum, and angular momentum from two-dimensional electron systems, focusing on metallic thin films described by the Drude conductivity. Using the Keldysh formalism within the…
The radial part of the wave function of an electron in a Coulomb potential is the product of a Laguerre polynomial and an exponential with the variable scaled by a factor depending on the degree. This note presents an elementary proof of…
We demonstrate a new method for the calculation of inelastic scattering cross-section, which in contrary to the Regge-based methods takes into account the energy momentum conservation law. By virtue of this method it was shown that the main…
The Pauli method of quantizing the Hydrogen system using the Runge-Lenz vector is ingenious. It is well known that the energy spectrum is identical with the one obtained from the Schr\"{o}dinger equation and the consistency contributed…
The two-dimensional Levinson theorem for the Klein-Gordon equation with a cylindrically symmetric potential $V(r)$ is established. It is shown that $N_{m}\pi=\pi (n_{m}^{+}-n_{m}^{-})= [\delta_{m}(M)+\beta_{1}]-[\delta_{m}(-M)+\beta_{2}]$,…