Related papers: Hydrogen Atom in Electric and Magnetic Fields: Dyn…
It is shown that the two-axis countertwisting Hamiltonian is exactly solvable when the quantum number of the total angular momentum of the system is an integer after the Jordan-Schwinger (differential) boson realization of the SU(2)…
At present, there are many methods of quantum entanglement of particles with an electromagnetic field. Most methods have a low probability of quantum entanglement and not an exact theoretical apparatus based on an approximate solution of…
The problem of a spinless particle subject to a general mixing of vector and scalar inversely linear potentials in a two-dimensional world is analyzed. Exact bounded solutions are found in closed form by imposing boundary conditions on the…
Two super-integrable and super-separable classical systems which can be considered as deformations of the harmonic oscillator and the Smorodinsky-Winternitz in two dimensions are studied and identified with motions in spaces of constant…
We consider the spectral problem for the two-dimensional Schr\"odinger operator for a charged particle in strong uniform magnetic and periodic electric fields. The related classical problem is analyzed first by means of the…
The hydrogen molecule can be used for determination of physical constants and for improved tests of the hypothetical long range force between hadrons, which requires a sufficiently accurate knowledge of the molecular levels. For this…
When a hydrogen-like atom is treated as a two dimensional system whose configuration space is multiply connected, then in order to obtain the same energy spectrum as in the Bohr model the angular momentum must be half-integral.
Pauli first noticed the hidden SO(4) symmetry for the Hydrogen atom in the early stages of quantum mechanics [1]. Departing from that symmetry, one can recover the spectrum of a spinless hydrogen atom and the degeneracy of its states…
General analytical solutions of the Quantum Hamilton Jacobi Equation for conservative one-dimensional or reducible motion are presented and discussed. The quantum Hamilton's characteristic function and its derivative, i.e. the quantum…
Semiclassical oscillation of the electron through the nucleus of the H atom yields both the exact energy and the correct orbital angular momentum for l=0 quantum states. Similarly, electron oscillation through the nuclei of H2+ accounts for…
Schrodinger's equation predicts something very peculiar about the electron in the Hydrogen atom: its total energy must be equal to zero. Unfortunately, an analysis of a zero-energy wavefunction for the electron in the Hydrogen atom has not…
The Schr\"odinger theory of electrons in an external electromagnetic field can be described from the perspective of the individual electron via the `Quantal Newtonian' laws (or differential virial theorems). These laws are in terms of…
We consider Schr\"odinger operator in dimension $d\ge 2$ with a singular interaction supported by an infinite family of concentric spheres, analogous to a system studied by Hempel and coauthors for regular potentials. The essential spectrum…
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…
We revisit the longstanding electromagnetic mass problem from a modern quantum field theory perspective. Focusing on a system of two widely separated hydrogen atoms, one in an excited $nS$ state and the other in the ground $1S$ state, we…
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 Born-Infeld form of the hydrogen atom has a spectrum that can be used to determine the physical viability of the theory, and place an experimentally relevant bound on the single parameter found in it. We compute this spectrum using the…
Extending the Feynman-Kleinert variational approach, we calculate the temperature-dependent effective classical potential governing the quantum statistics of a hydrogen atom in a uniform magnetic at all temperatures. The zero-temperature…
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…
A recently proposed algorithm to obtain global solutions of the double confluent Heun equation is applied to solve the quantum mechanical problem of finding the energies and wave functions of a particle bound in a potential sum of a…