Related papers: Quantum Electrodynamics of the Helium Atom
In this work, Rydberg energy levels of the triatomic hydrogen molecule ($\rm{H_3}$) are studied with multichannel quantum-defect theory. We extract the body-frame p-wave quantum defects from highly accurate \emph{ab initio} electronic…
In this work we reexamine quantum electrodynamics of atomic eletrons in the Coulomb gauge in the dipole approximation and calculate the shift of atomic energy levels in the context of Dalibard, Dupont-Roc and Cohen-Tannoudji (DDC) formalism…
Molecular helium represents a benchmark system for testing $\textit{ab initio}$ calculations on few-electron molecules. We report on the determination of the adiabatic ionization energy of the $a\,^3\Sigma_u^+$ state of He$_2$,…
Deeply bound KNN, KNNN and KNNNN states are discussed. The effective force exerted by the K meson on the nucleons is calculated with static nucleons. Next the binding energies are obtained by solving the Schrodinger equation or by…
We derive a full formula for the energy level of a heavy quarkonium state identified by the quantum numbers $n$, $\ell$, $s$ and $j$, up to ${\cal O}(\alpha_s^5 m)$ and ${\cal O}(\alpha_s^5 m \log \alpha_s)$ in perturbative QCD. The QCD…
The model-QED-operator approach [Phys. Rev. A 88, 012513 (2013)] to calculations of the radiative corrections to binding and transition energies in atomic systems is extended to the range of nuclear charges $110 \leqslant Z \leqslant 170$.…
Accurate predictions for hydrogen molecular levels require the treatment of electrons and nuclei on an equal footing. While nonrelativistic theory has been effectively formulated this way, calculation of relativistic and quantum…
The Schr\"odinger equation relates the electron wavefunction and the electric potential, which are emergent physical quantities. At that emergent level, the Schr\"odinger equation is either postulated as a principle of quantum physics or…
For quasiexactly solvable (QES) potentials a certain number of wave functions and energy levels can be analytically calculated. The complexity of an explicit calculation of the energy levels grows with the dimension of the QES sector. For a…
Effective potentials of the relativistic m\alpha^6 order correction for the ground state of the Coulomb two-center problem are calculated. They can be used to evaluate the relativistic contribution of that order to the energies of hydrogen…
We perform ab initio QED calculations of energy levels for the $n=1$ and $n=2$ states of He-like ions with the nuclear charge in the range $Z = 12$-100. The complete set of two-electron QED corrections is evaluated to all orders in the…
We have developed a simple method to solve anharmonic oscillators equations. The idea of our method is mainly based on the partitioning of the potential curve into (n+1) small intervals, solving the Schr\"odinger equation in each…
We present an exact calculation of the single-electron energies and wave-functions for any bound state in a realistic Si-SiO2 spherical quantum dot, including the material dependence of the electron effective mass. The influence of dot…
An infinite sequence of potential well functions is considered. A trial wavefunction is used with the Schr$\ddot{\text{o}}$dinger equation to obtain an approximate ground state energy for each potential well function. We obtain an…
We derive quantum electrodynamics corrections to the fine structure in three-electron atomic systems at $m \alpha^6$ and $m \alpha^7 \ln \alpha$ orders and present their numerical evaluations for the Li atom and Be$^+$ ion.
The electron-electron interaction correction of first order in $1/Z$ to the one-electron part of the nuclear recoil effect on binding energies in atoms and ions is considered within the framework of the rigorous QED approach. The…
An exact quantization rule for the Schr\"{o}dinger equation is presented. In the exact quantization rule, in addition to $N\pi$, there is an integral term, called the quantum correction. For the exactly solvable systems we find that the…
Precise numerical calculation of radiofrequency intervals between hyperfine sublevels of the $(37,35)$ state of the antiprotonic helium-4 atom is presented. Theoretical consideration includes the QED corrections of order $m\alpha^6$ to the…
We find approximate analytical presentation of the solutions $\Psi(r_1, r_2, r_{12})$ of Schr\"odinger equation for two-electron system bound by the nucleus, in the space region $r_{1,2}=0$ and $r_{12}=0$ that are of great importance for a…
The Schr\"odinger theory of electrons in an external electromagnetic field can be described from the perspective of the individual electron via the `Quantal Newtonian' laws (or differential virial theorems). These laws are in terms of…