Related papers: Analytic study of conformable Schrodinger equation…
A partial separation of the variables is practicable for the solution of Schroedinger's temporally independent equation in cartesian coordinates x,y,z, which yields moderately simple algebraic formulae for the amplitude functions involving…
As a serious attempt for constructing a new foundation for describing micro-entities from a causal standpoint, it was explained before in [1, 2, 3] that by unifying the concepts of information, matter and energy, each micro-entity is…
We consider the time evolution of the occupation probabilities for the 2s-2p transition in a hydrogen atom interacting with an external field, V(t). A two-state model and a dipole approximation are used. In the case of degenerate energy…
In this paper, we solve analytically the Schrodinger equation for s-wave and arbitrary angular momenta with the Hua potential is investigated respectively. The wave function as well as energy equation are obtained in an exact analytical…
Based on an exposition of the underlying physics and applied mathematics in arXiv:1603.00899, this paper in five separate parts presents a description of the properties of the amplitude functions of the hydrogen atom according to wave…
F. Gygi recently suggested an analytic, norm-conserving, regularized nuclear potential to enable all-electron plane-wave calculations [J. Chem. Theory Comput. 2023, 19, 1300--1309]. This potential $V(r)$ is determined by inverting the…
Exact solution of Schrodinger equation for the pseudoharmonic potential is obtained for an arbitrary angular momentum. The energy eigenvalues and corresponding eigenfunctions are calculated by Nikiforov-Uvarov method. Wavefunctions are…
We generalize the known solution of the Schr\"odinger equation, describing a particle confined to a triangular area, for a triangular graphene quantum dot with armchair-type boundaries. The quantization conditions, wave functions, and the…
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…
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…
We present a direct ab initio solution of the Schrodinger equation for neutral helium and helium-like atoms that reproduces the energy of the singlet S state 1S0. By redefining the two-electron wavefunction with tools from complex analysis…
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…
Wave functions of a new functional kind have been proposed for Helium-like atoms in this work . These functions explicitly depend on interelectronic and hyperspherical coordinates. The best ground state energy for the Helium atom $…
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…
Using singlet S states of the helium atom as an example, I describe precise calculation of energy levels in few-electron atoms. In particular, a complete set of effective operators is derived which generates O(m*alpha^6) relativistic and…
We demonstrate that the finiteness of the limiting values of the lower energy levels of a hydrogen atom under an unrestricted growth of the magnetic field, into which this atom is embedded, is achieved already when the vacuum polarization…
The hydrogen plasma is studied at temperatures T ~ 10^4 - 10^6 K using the free energy minimization method. A simple analytic free energy model is proposed which is accurate at densities up to 1 g/cc and yields convergent internal partition…
The electric dipole polarizabilities of $^3$H, $^3$He, and $^4$He are calculated directly using the Schr\"odinger equation with the latest generation of two- and three-nucleon interactions. These polarizabilities are necessary in order to…
The low energy scattering of heavy positively charged particles on hydrogen atoms (H) are investigated by solving the Faddeev equations in configuration space. A resonant value of the pH scattering length, $a=750\pm 5$ a.u., in the pp…
In this work we define single-particle potentials for a positron and a positronium atom interacting with light atoms (H, He, Li and Be) by inverting a single-particle Schr\"odinger equation. For this purpose, we use accurate energies and…