Related papers: The Hydrogen Atom, Pi and Lerch's Transcendent
We compute trace anomaly contribution to hydrogen atom mass, which turns out to be related to the part of the Lamb shift. This finding might shed new light on our understandings of the mass structure of QCD bound states, such as, proton.
The solution of Dirac's equation for the hydrogen atom according to relativistic wave mechanics yields for each state a vectorial amplitude function with four components, two large and two small. Each such component has its characteristic…
We investigated the hydrogen atom problem with deformed Heisenberg algebra leading to the existence of minimal length. Using modified perturbation theory developed in our previous work [M. M. Stetsko and V. M. Tkachuk, Phys. Rev. A 74,…
We present a general procedure to generate infinitely many BBP and BBP-like formulas for the simplest transcendental numbers. This provides some insight and a better understanding into their nature. In particular, we can derive the main…
We consider a hydrogen atom in the background spacetimes generated by an infinitely thin cosmic string and by a point-like global monopole. In both cases, we find the solutions of the corresponding Dirac equations and we determine the…
We consider the noncommutative algebra which is rotationally invariant. The hydrogen atom is studied in a rotationally invariant noncommutative space. We find the corrections to the energy levels of the hydrogen atom up to the second order…
Being comparable in quantum systems makes it possible for spaces with varying dimensions to attribute each other using special conversions can attribute schrodinger equation with like-hydrogen atom potential in defined dimensions to a…
As the simplest atom in nature, the hydrogen atom has been explored thoroughly from the perspective of non-relativistic quantum mechanics to relativistic quantum mechanics. Among the research on hydrogen atom, its energy level is the most…
The connection between the quantum frequency of radiation by the transition of the electron from orbit n to orbit k and frequencies of circling of electron in these orbits for the atom of hydrogen is determined.
We consider the energy levels of a hydrogen-like atom in the framework of $\theta $-modified, due to space noncommutativity, Dirac equation with Coulomb field. It is shown that on the noncommutative (NC) space the degeneracy of the levels…
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…
A famous pre-Newtonian formula for $\pi$ is obtained directly from the variational approach to the spectrum of the hydrogen atom in spaces of arbitrary dimensions greater than one, including the physical three dimensions.
We extend a method (E. Canc\`es and L.R. Scott, SIAM J. Math. Anal., 50, 2018, 381--410) to compute more terms in the asymptotic expansion of the van der Waals attraction between two hydrogen atoms. These terms are obtained by solving a set…
We consider a prototype polyene chain: donor-$\pi$(bridge)-acceptor. The distance between the donor and the acceptor is varied by increasing the number of bridged atoms and rate of electron transfer, k$_{et}$ is studied for a series 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 use of the Euler-Maclaurin formula and new derived uniform asymptotic expansions for the numerical evaluation of the Lerch transcendent $\Phi(z, s, a)$ for $z, s, a \in \mathbb{C}$ to arbitrary precision. A detailed analysis…
Isolated electrons resting above a helium surface are predicted to have a bound spectrum corresponding to a one-dimensional hydrogen atom. But in fact, the observed spectrum is closer to that of a quantum-defect atom. Such a model is…
In this short paper Euler gives a highly convergent series for arctan and thus pi, which converges much faster than the Leibniz series for arctan.
Analytical approximations are constructed for binding energies, quantum-mechanical sizes and oscillator strengths of main radiative transitions of hydrogen atoms arbitrarily moving in magnetic fields 10^{12}-10^{13} G. Examples of using the…
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…