Related papers: Schr\"odinger equation solved for the hydrogen mol…
We present algebraic derivation of the result of Schr\"{o}dinger [1] for the spectrum of hydrogen atom in the space with constant curvature.
We verify that the van der Waals interaction and hence all dispersion interactions for the hydrogen molecule given by: W"= -{A/R^6}-{B/R^8}-{C/R^10}- ..., in which R is the internuclear separation, are exactly soluble. The constants…
The configuration interaction approach provides a conceptually simple and powerful approach to solve the Schr\"odinger equation for realistic molecules and materials but is characterized by an unfavourable scaling, which strongly limits its…
A simple exactly solvable kinetic model for the non-linear inelastic hard sphere Boltzmann equation is used to explore the relevance of hydrodynamics for a granular gas. The equation predicts a non-trivial homogeneous cooling state (HCS),…
Schr\"odinger equation with given, {\it a priori} known current is formulated. A non-zero current density is maintained in the quantum system via a subsidiary condition imposed by vector, local Lagrange multiplier. Constrained minimization…
Considered is the Schr\"odinger equation in a finite-dimensional space as an equation of mathematical physics derivable from the variational principle and treatable in terms of the Lagrange-Hamilton formalism. It provides an interesting…
We provide a glimpse of recent progress in hadron physics made using QCD's Dyson-Schwinger equations, reviewing: the notion of in-hadron condensates and a putative solution of a gross problem with the cosmological constant; the dynamical…
Precision spectroscopy on cold molecules can potentially enable novel tests of fundamental laws of physics and alternative determination of some fundamental constants. Realizing this potential requires a thorough understanding of the…
The hydrogen molecule has become a test ground for quantum electrodynamical calculations in molecules. Expanding beyond studies on stable hydrogenic species to the heavier radioactive tritium-bearing molecules, we report on a measurement of…
We note that presenting Hydrogen atom Schrodinger equation in the case of arbitrary dimensions require simultaneous modification of the Coulomb potential that only in three dimensions has the form Z/r . This was not done in a number of…
The method and status of a study to provide numerical, high-precision values of the self-energy level shift in hydrogen and hydrogen-like ions is described. Graphs of the self energy in hydrogen-like ions with nuclear charge number between…
For the first time, the general nonlinear Schr\"odinger equation is investigated, in which the chromatic dispersion and potential are specified by two arbitrary functions. The equation in question is a natural generalization of a wide class…
By introducing and solving two correlative constrained variational problems as well as spectrum analysis, an approach to fix soliton frequency from the prescribed mass for nonlinear Schr\"odinger equations is found, and an open problem in…
Properties of the fractional Schrodinger equation have been studied. We have proven the hermiticity of fractional Hamilton operator and established the parity conservation law for the fractional quantum mechanics. As physical applications…
The full-dimensional time-dependent Schrodinger equation for the electronic dynamics of single-electron systems in intense external fields is solved directly using a discrete method. Our approach combines the finite-difference and Lagrange…
Modifications of Heisenberg's uncertainty relations have been proposed in the literature which imply a minimum position uncertainty. We study the low energy effects of the new physics responsible for this by examining the consequent change…
The quark-gluon sea in the hadrons is considered as periodically correlated. Energy levels of Shrodinger equation with harmonic potential is used for describing of the spectrum of hadron masses. In the considered cases the effective…
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…
A compact, few-parametric, physically adequate, 3-term variational trial function is used to calculate with high accuracy the energy of the ground state ${}^3\Pi_u$ of the hydrogen molecule ${\rm H}_2$ in strong magnetic field ${\bf B}$ in…
A theoretical comparison of the electronic excitation and ionisation behaviour of molecular hydrogen oriented either parallel or perpendicular to a linear polarised laser pulse is performed. The investigation is based on a non-perturbative…