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A detailed study of the lowest states $1s_0, 2p_{-1}, 2p_0$ of the hydrogen atom placed in a magnetic field $Bin(0-4.414times 10^{13} {rm G})$ and their electromagnetic transitions ($1s_{0} leftrightarrow 2p_{-1}$ and $ 1s_{0} leftrightarrow 2p_{0}$) is carried out in the Born Oppenheimer approximation. The variational method is used with a physically motivated recipe to design simple trial functions applicable to the whole domain of magnetic fields. We show that the proposed functions yield very accurate results for the ionization (binding) energies. Dipole and oscillator strengths are in good agreement with results by Ruder {em et al.} cite{Ruderbook} although we observe deviations up to $sim 30%$ for the oscillator strength of the (linearly polarized) electromagnetic transition $1s_{0} leftrightarrow 2p_{0}$ at strong magnetic fields $Bgtrsim 1000$ a.u.
We obtain the following analytical formula which describes the dependence of the electric potential of a point-like charge on the distance away from it in the direction of an external magnetic field B: Phi(z) = e/|z| [ 1- exp(-sqrt{6m_e^2}|z|) + exp(
It is shown that hydrogen atom is a unique object in physics having negative energy of electric field, which is present in the atom. This refers also to some hydrogen-type atoms: hydrogen anti-atom, atom composed of proton and antiproton, and positronium.
A simple locally accurate uniform approximation for the nodeless wavefunction is constructed for a {it neutral} system of two Coulomb charges of different masses $(-q,m_1)$ and $(q,m_2)$ at rest in a constant uniform magnetic field for the states of
The correction to the wave function of the ground state in a hydrogen-like atom due to an external homogenous magnetic field is found exactly in the parameter $Zalpha$. The $j=1/2$ projection of the correction to the wave function of the $ns_{1/2}$ s
The S-matrix theory formulation of closed-orbit theory recently proposed by Granger and Greene is extended to atoms in crossed electric and magnetic fields. We then present a semiclassical quantization of the hydrogen atom in crossed fields, which su