Related papers: Prediction of many-electron wavefunctions using at…
The three-body Schr\"odinger equation of the H$_2^+$ hydrogen molecular ion with Coulomb potentials is solved in perimetric coordinates using the Lagrange-mesh method. The Lagrange-mesh method is an approximate variational calculation with…
We study wave equations with energy dependent potentials. Simple analytical models are found useful to illustrate difficulties encountered with the calculation and interpretation of observables. A formal analysis shows under which…
We calculate the hydrogen molecule ion from the two particle Schr"odinger equation. Therefore a very simple two particle basis set is chosen. We suggest this ansatz to be used to solve the "two electron one phonon" three particle…
In this work we propose a novel composite method for accurate calculation of the energies of many-electron atoms. The dominant contribution to the energy (pair energies) are calculated by using explicitly correlated factorisable coupled…
Quantum mechanical scalar particle with polarizability is considered in the presence of the Coulomb field. Separation of variables is performed with the use of Wigner $D$-functions, the radial system of 15 equations is reduced to a single…
We discuss the solutions of the Schroedinger equation for piecewise potentials, given by the harmonic oscillator potential for $\vert x\vert >a$ and an arbitrary function for $\vert x\vert <a$, using elementary methods. The study of this…
We make a comparison between the energy levels of the hydrogen atom, calculated by using standard methods, and that by using a modified Coulomb potential due to the interaction between the magnetic moments of the proton and electron. In…
We present a novel approach to calculating strong field ionization dynamics of multielectron molecular targets. Adopting a multielectron wavefunction ansatz based on field-free ab initio neutral and ionic multielectron states, a set of…
The Schr\"odinger equation and Bloch theorem are applied to examine a system of protons confined within a periodic potential, accounting for deviations from ideal harmonic behavior due to real-world conditions like truncated and…
Scattering of electromagnetic waves by many small particles of arbitrary shapes is reduced rigorously to solving linear algebraic system of equations bypassing the usual usage of integral equations. The matrix elements of this linear…
Electron correlation effects are essential for an accurate ab initio description of molecules. A quantitative a priori knowledge of the single- or multi-reference nature of electronic structures as well as of the dominant contributions to…
General theorem describing a relation between diagonal of one-electron density matrix and a certain class of many-electron ensembles of determinant states is proved. As a corollary to this theorem a constructive proof of sufficiency of…
A simple real-space model for the electron wavefunction is suggested, based on a transverse wave with helicity, rotating at mc^2/h. The mapping of the real two-dimensional vector phasor to the complex plane permits this to satisfy the…
Maxwell's equations in the vacuum can be formally cast in the form of Schr\"odinger's equation. Unfortunately, the vector to which this equation directly applies is not a wavefunction: its amplitude squared is not a probability density but…
Electron-electron correlation forms the basis of difficulties encountered in many-body problems. Accurate treatment of the correlation problem is likely to unravel some nice physical properties of matter embedded in this correlation. In an…
Smooth model potentials with parameters selected to reproduce the spectrum of one-electron atoms are used to approximate the singular Coulomb potential. Even when the potentials do not mimic the Coulomb singularity, much of the spectrum is…
A new solvable hyperbolic single wave potential is found by expanding the regular solution of the 1D Schr\"odinger equation in terms of square integrable basis. The main characteristic of the basis is in supporting an infinite tridiagonal…
The hydrogen molecule can be used for determination of physical constants and for improved tests of the hypothetical long range force between hadrons, which requires a sufficiently accurate knowledge of the molecular levels. For this…
The Bloch wavefunction leads either to mathematically impossible consequences or suggests that the ground state energy is a function of size and shape when the geometry of large crystals is considered in detail. It is incompatible with the…
One approximation is made to describe a M+1 electron many-body wavefunction by a M electron many-body wavefunction and a single electron wavefunction. Under this approximation, we have derived the Coulomb energy which relates the exciton…