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It is shown that Schr\"odinger equation with combination of three potentials U = - {\alpha} r^{-1} + {\beta} r + kr^{2}, Coulomb, linear and harmonic, the potential often used to describe quarkonium, is reduced to a bi-confluent Heun…
The hyperfine interaction in the ground state of a hydrogen atom of assumed radius $R$ is proportional to $-1/R^3$, raising the question of why the hyperfine interaction does not lead to collapse of hydrogen, or positronium. We approach the…
In calculating the energy corrections to the hydrogen levels we can identify two different types of modifications of the Coulomb potential $V_{C}$, with one of them being the standard quantum electrodynamics corrections, $\delta V$,…
At energies below the Coulomb barrier, the fusion excitation function for the $^{12}$C+$^{12}$C system shows prominent fine structures, whereas that for the $^{12}$C+$^{13}$C system behaves more smoothly as a function of energy. We…
In the past five years enormous progress has been made in the ab initio calculations of the optical response of electrons in semiconductors. The calculations include the Coulomb interaction between the excited electron and the hole left…
We investigate the properties of two interacting ultracold polar molecules described as distinguishable quantum rigid rotors, trapped in a one-dimensional harmonic potential. The molecules interact via a multichannel two-body contact…
Structural phase transitions and soft phonon modes pose a longstanding challenge to computing electron-phonon (e-ph) interactions in strongly anharmonic crystals. Here we develop a first-principles approach to compute e-ph scattering and…
A non-linear non-perturbative relativistic atomic theory introduces spin in the dynamics of particle motion. The resulting energy levels of Hydrogen atom are exactly same as the Dirac theory. The theory accounts for the energy due to…
We compute the ground state energy of atoms and quantum dots with a large number N of electrons. Both systems are described by a non-relativistic Hamiltonian of electrons in a d-dimensional space. The electrons interact via the Coulomb…
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…
We examine the interplay between electron correlations and phonons in an Anderson-Holstein impurity model with an Einstein phonon. When the phonons are slow compared to charge fluctuations (frequency $\omega_0 \ll U/2$, the onsite Coulomb…
We investigate a system of equally charged Coulomb-interacting particles confined to a toroidal helix in the presence of an external electric field. Due to the confinement, the particles experience an effective interaction that oscillates…
The oscillator parameter in nuclei is refitted to reproduce the available charge radius data. As an important improvement, we include the Coulomb term evaluated within the assumption of a uniformly charged sphere, and take into account the…
Quantum statistical systems, composed of atoms or molecules interacting with each other through highly singular non-integrable potentials, are considered. The treatment of such systems cannot start with the standard approximations such as…
We investigate the interaction of strongly correlated electrons with phonons in the frame of the Hubbard-Holstein model. The electron-phonon interaction is considered to be strong and is an important parameter of the model besides the…
The present work studies aspects of the electronic correlation in confined H$^{-}$, He and Li$^+$ atoms in their ground states using the informational entropies. In this way, different variational wavefunctions are employed in order of…
We numerically study the collective excitations present in isotropic superconductors including a screened Coulomb interaction. By varying the screening strength, we analyze its impact on the system. We use a formulation of the effective…
In the quantization scheme which weakens the hermiticity of a Hamiltonian to its mere PT invariance the superposition V(x) = x^2+ Ze^2/x of the harmonic and Coulomb potentials is defined at the purely imaginary effective charges (Ze^2=if)…
To understand the pressure-induced changes in the electronic structure and the electron-phonon interaction in yttrium, we have studied hexagonal close-packed (hcp) yttrium, stable at ambient pressure and double hexagonal close-packed (dhcp)…
He atom scattering has been demonstrated to be a sensitive probe of the electron-phonon interaction parameter $\lambda$ at metal and metal-overlayer surfaces. Here it is shown that the theory linking $\lambda$ to the thermal attenuation of…