Related papers: Comment on the shape of Hydrogen equation in space…
We substantiate the need for account of the proper electromagnetic field of the electron in the canonical problem of hydrogen in relativistic quantum mechanics. From mathematical viewpoint, the goal is equivalent to determination of the…
We discuss the tightly bound (hydrino) solution of the Klein-Gordon equation for the Coulomb potential in 3 dimensions. We show that a similarly tightly bound state occurs for the Dirac equation in 2 dimensions. These states are unphysical…
A two-dimensional hydrogen atom offers a promising alternative for describing the quantum interaction between an electron and a proton in the presence of a straight cosmic string. Reducing the hydrogen atom to two dimensions enhances its…
The screening of a Coulomb potential by superstrong magnetic field is studied. Its influence on the spectrum of a hydrogen atom is determined.
We prove that the set of singular times for weak solutions of the space homogeneous Landau equation with Coulomb potential constructed as in [C. Villani, Arch. Rational Mech. Anal. 143 (1998), 273-307] has Hausdorff dimension at most 1/2.
Using the approach the modified Euler-Lagrange field equation together with the corresponding Seiberg-Witten maps of the dynamical fields, a noncommutative Dirac equation with a Coulomb potential is derived. We then find the noncommutative…
The Shape invariant method has the algebraic structure and its algebras are infinite-dimensional. These algebras are converted into finite-dimensional under conditions. Based on the property of this method we obtain the algebraic structure…
It is well known that the Schr\"odinger equation is only suitable for the particle in common potential $V(\vec{r},t)$. In this paper, a general Quantum Mechanics is proposed, where the Lagrangian is the general form. The new quantum wave…
The Schrodinger equation for stationary states in a central potential is studied in an arbitrary number of spatial dimensions, say q. After transformation into an equivalent equation, where the coefficient of the first derivative vanishes,…
We present algebraic derivation of the result of Schr\"{o}dinger [1] for the spectrum of hydrogen atom in the space with constant curvature.
Quantum (and classical) binding energy considerations in n-dimensional space indicate that atoms (and planets) can only exist in three-dimensional space. This is why observable space is solely 3-dimensional. Both a novel Virial theorem…
We rewrite the time dependent Schr\"odinger equation by using only three dimensional vector algebra and by avoiding to introduce any complex numbers. We show that this equation leads to the same conclusions than the "complex version"…
It has been suggested that the high symmetries in the Schr\"odinger equation with the Coulomb or harmonic oscillator potentials may remain in the corresponding relativistic Dirac equation. If the principle is correct, in the Dirac equation…
The radial part of the wave function of an electron in a Coulomb potential is the product of a Laguerre polynomial and an exponential with the variable scaled by a factor depending on the degree. This note presents an elementary proof of…
In this work we calculate the correction to the ground state energy of the hydrogen atom due to contributions arising from the presence of a minimal length. The minimal length scenario is introduced by means of modifying the Dirac equation…
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 have obtained the uncertainty relations for arbitrary states of the hydrogen atom. It is shown that the minimal value of the uncertainty relation is attained for the circular Rydberg states.
In this paper we introduce a new model for the quantum-mechanical system of the hydrogen atom. We start with a four-dimensional Lorentzian quadratic space $(V,q)$ and let $C \subset V$ be the corresponding cone. The Hilbert space of our…
The van der Waals interaction between two polarizable atoms is considered. In three dimensions the standard form with an attractive $1/|R|^6$ potential is obtained from second-order quantum perturbation theory. When the electron motion is…
We study space-time noncommutativity applied to the hydrogen atom and its phenomenological effects. We find that it modifies the potential part of the Hamiltonian in such a way we get the Kratzer potential instead of the Coulomb one and…