Related papers: H^+_2$ in a strong magnetic field described via a …
Using the variational method, a detailed study of the lowest m = 0,-1 electronic states of the exotic molecular ion H_4^{3+} in a strong magnetic field, in the linear symmetric configuration parallel to the direction of the magnetic field…
Using a variational method we study a sequence of the one-electron atomic and molecular-type systems H, H_2^+, H_3^(2+) and H_4^(3+) in the presence of a homogeneous magnetic field ranging B = 0 - 4.414x10^{13} G. These systems are taken as…
We propose three effective Hamiltonians which approximate atoms in very strong homogeneous magnetic fields $B$ modelled by the Pauli Hamiltonian, with fixed total angular momentum with respect to magnetic field axis. All three Hamiltonians…
The bound state in the system of three protons and an electron (pppe) under a homogeneous strong magnetic field where the protons are situated in the vertices of an equilateral triangle perpendicular to the magnetic field lines is found. It…
The existence and stability of the linear hydrogenic chain H$_3$ and H${}_2^-$ in a strong magnetic field is established. Variational calculations for H$_3$ and H${}_2^-$ are carried out in magnetic fields in the range $10^{11}\leq B \leq…
The Dirac equation for H$_2^+$ is solved numerically by expansion in a basis set of two-center exponential functions, using different kinetic balance schemes. Very high precision (27-32 digits) is achieved, either with the dual kinetic…
We study the energy levels of H$_2$ molecules in a superstrong magnetic field ($B\go 10^{12}$ G), typically found on the surfaces of neutron stars. The interatomic interaction potentials are calculated by a Hartree-Fock method with…
We consider a non-relativistic two-dimensional (2D) hydrogen-like atom in a weak, static, uniform magnetic field perpendicular to the atomic plane. Within the framework of the Rayleigh-Schr\"odinger perturbation theory, using the Sturmian…
The $He^+$ ion on a plane subject to a constant magnetic field $B$ perpendicular to the plane is considered taking into account the finite nuclear mass. Factorization of eigenfunctions permits to reduce the four-dimensional problem to…
A detailed study of the ground state of the Coulomb system $(\al \al e e)$ which corresponds to the $He_2^{2+}$ molecular ion in a magnetic field $B=0-4.414 \times 10^{13} $ G in parallel configuration (infinitely massive $\al-$particles…
The problem of a hydrogen atom in a strong magnetic field is a notorious example of a quantum system that has genuinely different asymptotic behaviors in different directions. In the direction perpendicular to the magnetic field the motion…
A clear understanding of the mechanisms that control the electron dynamics in strong laser field is still a challenge that requires to be interpreted by advanced theory. Development of accurate theoretical and computational methods, able to…
Two dimensional massless Dirac Hamiltonian under the influence of hyperbolic magnetic fields is mentioned in curved space. Using a spherical surface parametrization, the Dirac operator on the sphere is presented and the system is given as…
In this paper we overview some results on the hydrogen atom in external static uniform magnetic fields. We focus on the case of very strong magnetic field, B>>B_0=2.3x10^9 Gauss, use various approximate models and, particularly, in the…
The existence of bound states of the system $(\al,e,e,e)$ in a magnetic field $B$ is studied using the variational method. It is shown that for $B \gtrsim 0.13\,{\rm a.u.}$ this system gets bound with total energy below the one of the…
The Coulombic systems $(\al p e)$ and $(\al\al e)$, $(\al p p e)$, $(\al \al p e)$ and $(Li^{3+} Li^{3+} e)$ placed in a magnetic field $B \gtrsim 10^{11} {G}$ are studied. It is demonstrated a theoretical existence of the exotic ion $(He…
We substantiate the need for account of the proper electromagnetic field of the electron in the canonical problem of hydrogen in relativistic quantum mechanics. From mathematical viewpoint, the goal is equivalent to determination of the…
We obtain exact solutions of the Klein-Gordon and Pauli Schroedinger equations for a two-dimensional hydrogen-like atom in the presence of a constant magnetic field. Analytic solutions for the energy spectrum are obtained for particular…
A two-dimensional (2D) hydrogen-like atom with a relativistic Dirac electron, placed in a weak, static, uniform magnetic field perpendicular to the atomic plane, is considered. Closed forms of the first- and second-order Zeeman corrections…
The well known hypervirial perturbation method (HPM)\ based on hypervirial relations and the Hellmann-Feynman theorem is suitable for the calculation of perturbation corrections of large order for the two-dimensional hydrogen-like atom in a…