Related papers: The hydrogen atom according to wave mechanics in c…
In this work, we consider the hydrogen atom confined inside a penetrable spherical potential. The confining potential is described by an inverted-Gaussian function of depth $\omega_0$, width $\sigma$ and centered at $r_c$. In particular,…
In this review we consider two different models of a hydrogenic atom in a quantized electromagnetic field that treat the electron relativistically. The first one is a no-pair model in the free picture, the second one is given by the…
A trajectory in the Schroedinger wave for an electron in an attractive Coulomb potential with the dynamical behavior is proposed and illustrated for a scattering and a bound state. The scattering cross section derived from the trajectories…
We derive some properties of the hydrogen atom inside a box with an impenetrable wall that have not been discussed before. Suitable scaling of the Hamiltonian operator proves to be useful for the derivation of some general properties of the…
The question of whether hydrogen atoms can exist or not in spaces with a number of dimensions greater than 3 is revisited, considering higher dimensional Euclidean spaces. Previous results which lead to different answers to this question…
In this article we develop in detail a causal model of the hydrogen atom, building on the earlier work of Dewdney and Malik [1] in which they outlined a causal model of the hydrogen atom, focusing more on a causal model of angular momentum…
The nonrelativistic quantum dynamics of a spinless charged particle in the presence of the Aharonov--Bohm potential in curved space is considered. We chose the surface as being a cone defined by a line element in polar coordinates. The…
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…
An ab initio, three-dimensional quantum mechanical calculation has been performed for the time-evolution of continuum electrons in the fields of moving charges. Here the essential singularity associated with the diverging phase factor in…
Monogenic functions in the algebra of 5-dimensional spacetime have been used previously by the author as first principle in different areas of fundamental physics; the paper recovers that principle applying it to the hydrogen atom. The…
We construct a system of coherent states for the hydrogen atom that is expressed in terms of elementary functions. Unlike to the previous attempts in this direction, this system possesses the properties equivalent to the most of those for…
The de Broglie-Bohm causal theory of quantum mechanics is applied to the hydrogen atom in the fully spin-dependent and relativistic framework of the Dirac equation, and in the nonrelativistic but spin-dependent framework of the Pauli…
An old result of A.F. Stevenson [Phys. Rev.} 59, 842 (1941)] concerning the Kepler-Coulomb quantum problem on the three-dimensional (3D) hypersphere is considered from the perspective of the radial Schr\"odinger equations on 3D spaces of…
For the $S$ states of two-electron atoms, we introduce an exact and unique factorization of the internal eigenfunction in terms of a marginal amplitude, which depends functionally on the electron-nucleus distances $r_1$ and $r_2$, and a…
We present a simple one-dimensional quantum-mechanical model for a particle attached to a surface. We solve the Schr\"odinger equation in terms of Weber functions and discuss the behavior of the eigenvalues and eigenfunctions. We derive the…
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…
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 differential probability of the process of Compton ionization of a hydrogen atom by a cylindrical electromagnetic wave is calculated taking into account the finite size of the target, which resulted in the appearance of a dependence of…
Time-dependent Schroedinger equation represents the basis of any quantum-theoretical approach. The question concerning its proper content in comparison to the classical physics has not been, however, fully answered until now. It will be…
A plane, monochromatic electromagnetic wave propagating in free space can have a certain amount of spin angular momentum but cannot possess any orbital angular momentum. Even the spin angular momentum of the plane-wave is difficult to…