The Relativistic Quantum Defect Orbital Method and some of its Applications

Martin, Immaculada

doi:10.1007/978-94-011-4894-8_4

Cited by 1 publication

(2 citation statements)

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“…In its second order form this equation differs very little from the nonrelativistic Schrödinger equation treated in (Kholodenko and Kauffman, 2019). Although not mentioned in just cited works, below we shall argue that calculations based on the perihelion shift (Burkhardt et al, 1992) and on use of the Dirac equation (Martin, 1997) are physically not too much different from each other. This fact is of fundamental significance.…”

Section: General Commentsmentioning

confidence: 81%

“…But mentioned results based on relativistic calculations known from the theory of theory of perihelion shift are not the only ones which can be used as point of departure. Another approach of computation of quantum defects coming very close to ideas and methods developed in (Kholodenko and Kauffman, 2019) is presented in (Karwowski and Martin,1991) and later, in (Martin, 1997). Both papers use Dirac equation in second order form as point of departure.…”

Section: General Commentsmentioning

confidence: 99%

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How the Modified Bertrand Theorem Explains Regularities and Anomalies of the Periodic Table of Elements

Kholodenko

2020

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Bertrand theorem permits closed orbits in 3d Euclidean space only for 2 types of central potentials. These are of Kepler-Coulomb and harmonic oscillator type. Volker Perlick recently extended Bertrand theorem. He designed new static spherically symmetric (Bertrand) spacetimes obeying Einstein's equations and supporting closed orbits. In this work we demonstrate that the topology and geometry of these spacetimes permits us to solve quantum many-body problem for any atom of periodic system exactly. The computations of spectrum for any atom are analogous to that for hydrogen atom. Initially, the exact solution of the Schrödinger equation for any multielectron atom (without reference to Bertrand theorem) was obtained by Tietz in 1956. We recalculated Tietz results by applying the methodology consistent with new (different from that developed by Fock in 1936) way of solving Schrödinger's equation for hydrogen atom. By using this new methodology it had become possible to demonstrate that the Tietz-type Schrödinger's equation is in fact describing the quantum motion in Bertrand spacetimes. As a bonus, we solved analytically the Löwdin's challenge problem. Obtained solution is not universal though since there are exceptions of the Madelung rule in transition metals and among lanthanides and actinides. Quantum mechanically these exceptions as well as the rule itself are treated thus far with help of relativistic Hartree-Fock calculations. The obtained results do not describe the exceptions in detail yet. However, studies outlined in this paper indicate that developed new methods are capable of describing exceptions as well. The paper ends with some remarks about usefulness of problems of atomic physics for development of quantum mechanics, quantum field theory and (teleparallel) gravity

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Section: General Commentsmentioning

confidence: 81%

Section: General Commentsmentioning

confidence: 99%