Related papers: High orders of the perturbation theory for hydroge…
The hydrogen atom in two dimensions, described by a Schr\"odinger equation with a Chern-Simons potential, is numerically solved. Both its wave functions and eigenvalues were determined for small values of the principal quantum number $n$.…
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 atom is a system amenable to an exact treatment within Schroedinger's formulation of quantum mechanics according to coordinates in four systems -- spherical polar, paraboloidal, ellipsoidal and spheroconical coordinates; the…
We leverage the power of neural quantum states to describe the ground state wave function of solid and liquid atomic hydrogen, including both electronic and protonic degrees of freedom. For static protons, the resulting Born-Oppenheimer…
Formulations of magnetic monopoles in a Hilbert-space formulation of quantum mechanics require Dirac's quantization condition of magnetic charge, which implies a large value that can easily be ruled out for elementary particles by standard…
For quantum mechanics of a charged particle in a classical external electromagnetic field, there is an apparent puzzle that the matrix element of the canonical momentum and Hamiltonian operators is gauge dependent. A resolution to this…
It is conjectured that Stark states of excited hydrogen atom posses magnetic charge for which the quantum mechanical operator is $${\cal G}_{op} = {e\over \hbar} (\vec\sigma\cdot\vec A)$$ where $\vec A$ is the Runge-Lenz vector. The…
The recently introduced reconciliation of the theories of special relativity and wave mechanics implies that the mass-energy equivalence principle must be expressed mathematically as H = mv^2, where H is the total energy of a particle, m is…
The screening of a Coulomb potential by superstrong magnetic field is studied. Its influence on the spectrum of a hydrogen atom is determined.
The influence of the finiteness of the proton radius and mass on the energies of a hydrogen atom and hydrogen-like ions in a superstrong magnetic field is studied. The finiteness of the nucleus size pushes the ground energy level up leading…
We calculate ionization energies and fundamental vibrational transitions for H$_2^+$, D$_2^+$, and HD$^+$ molecular ions. The NRQED expansion for the energy in terms of the fine structure constant $\alpha$ is used. Previous calculations of…
Heisenberg antiferromagnets in a strong uniform magnetic field $H$ are expected to exhibit a gapless phase with a global O(2) symmetry. In many real magnets, a small energy gap is induced by additional interactions that can be viewed as a…
The electronic structure of the ground and some excited states of neutral atoms with the nuclear charge numbers $1\leq Z \leq 10$ and their single positive ions are investigated by means of our 2D mesh Hartree-Fock method for strong…
A hierarchical ordering is demonstrated for the periodic orbits in a strongly coupled multidimensional Hamiltonian system, namely the hydrogen atom in crossed electric and magnetic fields. It mirrors the hierarchy of broken resonant tori…
The solution of Dirac's equation for the hydrogen atom according to relativistic wave mechanics yields for each state a vectorial amplitude function with four components, two large and two small. Each such component has its characteristic…
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…
The electronic structure of the hydrogen molecule is investigated for the parallel configuration. The ground states of the Sigma manifold are studied for ungerade and gerade parity as well as singlet and triplet states covering a broad…
The lowest bound states of the hydrogen negative ion and negative donor systems in a homogeneous magnetic field are investigated theoretically via a full configuration interaction approach with an anisotropic Gaussian basis set. The broad…
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 the hydrogen molecular ion $H^+_2$ in the presence of a strong homogeneous magnetic field. In this regime, the effective Hamiltonian is almost one dimensional with a potential energy which looks like a sum of two Dirac delta…