相关论文: Perturbative approach to the hydrogen atom in stro…
The states of hydrogen atom with principal quantum number $n\le3$ and zero magnetic quantum number in constant homogeneous magnetic field ${\cal H}$ are considered. The coefficients of energy eigenvalues expansion up to 75th order in powers…
Recurrence relations of perturbation theory for hydrogen ground state are obtained. With their aid polarizabilities in constant perpendicular electric and magnetic fields are computed up to 80th order. The high orders asymptotic is compared…
The order dependent mapping method, its convergence has recently been proven for the energy eigenvalue of the anharmonic oscillator, is applied to re-sum the standard perturbation series for Stark effect of the hydrogen atom. We perform a…
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…
The two-dimensional hydrogen-like atom in a constant magnetic field is considered. It is found that this is actually two separate problems. One for which the magnetic field causes an effective attraction between the nucleus and the electron…
A compact, few-parametric, physically adequate, 3-term variational trial function is used to calculate with high accuracy the energy of the ground state ${}^3\Pi_u$ of the hydrogen molecule ${\rm H}_2$ in strong magnetic field ${\bf B}$ in…
The Stark effect in hydrogen and the cubic anharmonic oscillator furnish examples of quantum systems where the perturbation results in a certain ionization probability by tunneling processes. Accordingly, the perturbed ground-state energy…
The O(4) supersymmetry of the hydrogen atom is utilized to construct a complete basis using only the bound state wave functions. For a large class of perturbations, an expansion of the electron (exciton) wave function into such a complete…
We study energy spectrum for hydrogen atom with deformed Heisenberg algebra leading to minimal length. We develop correct perturbation theory free of divergences. It gives a possibility to calculate analytically in the 3D case the…
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 hydrogen atom perturbed by a constant 1-dimensional weak quadratic potential $\lambda z^2$ is solved at first-order perturbation theory using the eigenstates of the total angular momentum operator - the coupled basis. Physical…
The first order perturbations of the energy levels of a hydrogen atom in central internal gravitational field are investigated. The internal gravitational field is produced by the mass of the atomic nucleus. The energy shifts are calculated…
Highly accurate variational calculations, based on a few-parameter, physically adequate trial function, are carried out for the hydrogen molecule \hh in inclined configuration, where the molecular axis forms an angle $\theta$ with respect…
For the hydrogen atom in combined magnetic and electric fields we investigate the dependence of the quantum spectra, classical dynamics, and statistical distributions of energy levels on the mutual orientation of the two external fields.…
It is well known that quantum-mechanical perturbation theory often give rise to divergent series that require proper resummation. Here I discuss simple ways in which these divergences can be avoided in the first place. Using the elementary…
A detailed study of the lowest states $1s_0, 2p_{-1}, 2p_0$ of the hydrogen atom placed in a magnetic field $B\in(0-4.414\times 10^{13} {\rm G})$ and their electromagnetic transitions ($1s_{0} \leftrightarrow 2p_{-1}$ and $ 1s_{0}…
Adaptive perturbation is a new method for perturbatively computing the eigenvalues and eigenstates of quantum mechanical Hamiltonians that heretofore were not believed to be obtainable by such methods. The novel feature of adaptive…
In this paper we present a perturbation theory for constant quaternionic potentials. The effects of quaternionic perturbations are explicitly treated for bound states of hydrogen atom, infinite potential well and harmonic oscillator.…
The magnetic moments of ${}^2{H}$, ${}^3{He}$ and ${}^3{H}$ as well as the thermal neutron capture rate on the proton are calculated using heavy baryon chiral perturbation theory {\it \`{a} la} Weinberg. The M1 operators have been derived…
Symmetry restoration in a theory of a self-interacting charged scalar field at finite temperature and in the presence of an external magnetic field is examined. The effective potential is evaluated nonperturbatively in the context of the…