Related papers: On the quantisation of the angular momentum
We present in this work a pedagogical way of quantizing the atomic orbit for the hydrogen's atom model proposed by Bohr without using his hypothesis of angular momentum quantization. In contrast to the usual treatment for the orbital…
We study the Hydrogen atom as a quantum mechanical system with a Coulomb like potential, with a semiclassical approach based on an effective description of quantum mechanics. This treatment allows us to describe the quantum state of 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…
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 revisit the quantum-mechanical two-dimensional hydrogen atom with an electric field confined to a circular box of impenetrable wall. In order to obtain the energy spectrum we resort to the Rayleigh-Ritz method with a polynomial basis…
Hydrogen atom is studied as a quantum-classical hybrid system, where the proton is treated as a classical object while the electron is regarded as a quantum object. We use a well known mean-field approach to describe this hybrid hydrogen…
The Dirac equation offers a precise analytical description of relativistic two-particle bound states, when one of the constituent is very heavy and radiative corrections are neglected. Looking at the high-Z hydrogen-like atom in the…
We show that the spectrum of orbital angular momentum in quantum mechanics consists of two parts when the underlying space has periodic boundaries. While the first part consists of the usual textbook integer quantized values, the second is…
We construct wave packets for the hydrogen atom labelled by the classical action-angle variables with the following properties. i) The time evolution is exactly given by classical evolution of the angle variables. (The angle variable…
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…
Real atomic systems, like the hydrogen atom in a magnetic field or the helium atom, whose classical dynamics are chaotic, generally present both discrete and continuous symmetries. In this letter, we explain how these properties must be…
Reaching ultimate performance of quantum technologies requires the use of detection at quantum limits and access to all resources of the underlying physical system. We establish a full quantum analogy between the pair of angular momentum…
In Part one of this Paper a hypothesis is forwarded of the electron charge in an atom existing in a distributed form. To check it by methods of electrodynamics and mechanics (without invoking the formalism of quantum mechanics and the…
A partial separation of the variables is practicable for the solution of Schroedinger's temporally independent equation in cartesian coordinates x,y,z, which yields moderately simple algebraic formulae for the amplitude functions involving…
We examine the procedure to construct the variables of use for the momentum representation in quantum mechanics. The momentum variables must be chosen properly conjugate to the corresponding position space variables, such that valid…
We show how strongly correlated ultracold bosonic atoms loaded in specific orbital angular momentum states of arrays of cylindrically symmetric potentials can realize a variety of spin-1/2 models of quantum magnetism. We consider explicitly…
The hydrogen atom as relativistic bound-state system of a proton and an electron in the complex-mass scheme is investigated. Interaction of a proton and an electron in the atom is described by the Lorentz-scalar Coulomb potential; the…
For a charge-monopole pair, though the definition of the orbital angular momentum is different from the usual one, and the transverse part of the momentum that includes the vector potential as an additive term turns out to be the so-called…
To describe a relativistic hydrogen atom we used the Poincare-covariant model of a two particle system with gauge invariant potential. The kernel of the radial integral equation is obtained which describes a system of two fermions with…
We deduce the quantization of the atomic orbit for the hydrogen's atom model proposed by Bohr without using his hypothesis of angular momentum quantization. We show that his hypothesis can be deduced from and is a consequence of the…