It has been long known that a year after Schrödinger published his equation, Madelung also published a hydrodynamics version of Schrödinger equation. Quantum diffusion is studied via dissipative Madelung hydrodynamics. Initially the wave packet spreads ballistically, than passes for an instant through normal diffusion and later tends asymptotically to a sub‐diffusive law. In this paper we will review two different approaches, including Madelung hydrodynamics and also Bohm potential. Madelung formulation leads to diffusion interpretation, which after a (...) generalization yields to Ermakov equation. Since Ermakov equation cannot be solved analytically, then we try to find out its solution with Mathematica package. It is our hope that these methods can be verified and compared with experimental data. But we admit that more researches are needed to fill all the missing details. (shrink)

This article considers two important traditions concerning the chemical elements. The first is the meaning of the term “element” including the distinctions between element as basic substance, as simple substance and as combined simple substance. In addition to briefly tracing the historical development of these distinctions, I make comments on the recent attempts to clarify the fundamental notion of element as basic substance for which I believe the term “element” is best reserved. This discussion has focused on the writings of (...) Fritz Paneth which are here analyzed from a new perspective. The other tradition concerns the reduction of chemistry to quantum mechanics and an understanding of chemical elements through their microscopic components such as protons, neutrons and electrons. I claim that the use of electronic configurations has still not yet settled the question of the placement of several elements and discuss an alternative criterion based on maximizing triads of elements. I also point out another possible limitation to the reductive approach, namely the failure, up to now, to obtain a derivation of the Madelung rule. Mention is made of some recent similarity studies which could be used to clarify the nature of ‘elements’. Although it has been suggested that the notion of element as basic substance should be considered in terms of fundamental particles like protons and electrons, I resist this move and conclude that the quantum mechanical tradition has not had much impact on the question of what is an element which remains an essentially philosophical issue. (shrink)

We describe here a series of experimental analogies between fluid mechanics and quantum mechanics recently discovered by a team of physicists. These analogies arise in droplet systems guided by a surface (or pilot) wave. We argue that these experimental facts put ancient theoretical work by Madelung on the analogy between fluid and quantum mechanics into new light. After re-deriving Madelung’s result starting from two basic fluid-mechanical equations (the Navier-Stokes equation and the continuity equation), we discuss the relation with (...) the de Broglie-Bohm theory. This allows to make a direct link with the droplet experiments. It is argued that the fluid-mechanical interpretation of quantum mechanics, if it can be extended to the general N-particle case, would have an advantage over the Bohm interpretation: it could rid Bohm’s theory of its strongly non-local character. (shrink)

At the heart of chemistry lies the periodic system of chemical elements. Despite being the cornerstone of modern chemistry, the overall structure of the periodic system has never been fully understood from an atomic physics point of view. Group-theoretical models have been proposed instead, but they suffer from several limitations. Among others, the identification of the correct symmetry group and its decomposition into subgroups has remained a problem to this day. In an effort to deepen our limited understanding of the (...) periodic law, we have extended the traditional Lie algebraic framework to account for the peculiar degeneracy structure of the periodic system. Starting from the four-dimensional hidden symmetry and accidental degeneracy of the hydrogen atom, as first revealed by Fock in 1935, our research has mainly focussed on the way this SO(4) symmetry of the Coulomb potential gets broken in the periodic system as a consequence of the transformation of the hydrogenic (n, l) filling order to the Madelung (n+l, n) order due to electronic repulsions, relativistic effects and spin-orbit couplings. In this PhD dissertation, a new left-step format of the periodic table is first proposed on the basis of the Madelung rule. Following the particle physics tradition, the chemical elements are then considered as various states of some 'atomic matter', which is described by a non-compact spectrum-generating dynamical Lie group. The chemical elements are shown to form a basis for a single infinite-dimensional degeneracy space of the SO(4,2) ⊗ SU(2) group. An explanation for the period doubling is then proposed in terms of a particular symmetry breaking of the SO(4,2) group to the anti de Sitter SO(3,2) group. The Madelung rule is rationalised on the basis of nonlinear Lie algebras which reflect the screening of the Coulomb hole. This opens new perspectives for a symmetry-based understanding of how the periodic law emerges from its quantum mechanical foundations, and holds the future promise of complementing our current phenomenological approach by a direct atomic physics approach. (shrink)

To this day, a hundred and fifty years after Mendeleev's discovery, the overal structure of the periodic system remains unaccounted for in quantum-mechanical terms. Given this dire situation, a handful of scientists in the 1970s embarked on a quest for the symmetries that lie hidden in the periodic table. Their goal was to explain the table's structure in group-theoretical terms. We argue that this symmetry program required an important paradigm shift in the understanding of the nature of chemical elements. The (...) idea, in essence, consisted of treating the chemical elements, not as particles, but as states of a superparticle. We show that the inspiration for this came from elementary particle physics, and in particular from Heisenberg's suggestion to treat the proton and neutron as different states of the nucleon. We provide a careful study of Heisenberg's last paper on the nature of elementary particles, and explain why the Democritean picture of matter no longer applied in modern physics and a Platonic symmetry-based picture was called for instead. We show how Heisenberg's Platonic philosophy came to dominate the field of elementary particle physics, and how it found its culmination point in Gell-Mann's classification of the hadrons in the eightfold way. We argue that it was the success of Heisenberg's approach in elementary particle physics that sparked the group-theoretical approach to the periodic table. We explain how it was applied to the set of chemical elements via a critical examination of the work of the Russian mathematician Abram Ilyich Fet the Turkish-American physicist Asim Orhan Barut, before giving some final reflections. (shrink)