The Canonical Form of the Rabi Hamiltonian

The Rabi Hamiltonian, describing the coupling of a two-level system to a single quantized boson mode, is studied in the Bargmann-Fock representation. The corresponding system of differential equations is transformed into a canonical form in which all regular singularities between zero and infinity have been removed. The canonical or Birkhoff-transformed equations give rise to a two-dimensional eigenvalue problem, involving the energy and a transformational parameter which affects the coupling strength. The known isolated exact solutions of the Rabi Hamiltonian are found to correspond to the uncoupled form of the canonical system.Comment: 17 pages, LaTeX, no figures, to appear in J.Math.Phy

Particular Symmetries: Group Theory of the Periodic System

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

Coacher’s labor problems as an element of high class sportsmen training

В работе рассматривается такая научная область, как спорт высших достижений. Предлагается определение тренерского труда, также выделяются основные проблемы реализации тренерского труда.In this article we consider such scientific area as high performance sport. Definition of coaching labor is proposing also we highlight main problems of coaching labor realization

The Exponentially Weighted Moving Average Procedure for Detecting Changes in Intensive Longitudinal Data in Psychological Research in Real-Time:A Tutorial Showcasing Potential Applications

Affect, behavior, and severity of psychopathological symptoms do not remain static throughout the life of an individual, but rather they change over time. Since the rise of the smartphone, longitudinal data can be obtained at higher frequencies than ever before, providing new opportunities for investigating these person-specific changes in real-time. Since 2019, researchers have started using the exponentially weighted moving average (EWMA) procedure, as a statistically sound method to reach this goal. Real-time, person-specific change detection could allow (a) researchers to adapt assessment intensity and strategy when a change occurs to obtain the most useful data at the most useful time and (b) clinicians to provide care to patients during periods in which this is most needed. The current paper provides a tutorial on how to use the EWMA procedure in psychology, as well as demonstrates its added value in a range of potential applications.</p

The Boron Buckyball has an Unexpected Th Symmetry

The boron buckyball avoids the high symmetry icosahedral cage structure. The previously reported Ih symmetric structure is not an energy minimum in the potential energy surface and exhibits a spontaneous symmetry breaking to yield a puckered cage with a rare Th symmetry. The HOMO-LUMO gap is twice as large as the reported value and amounts to 1.94 eV at B3LYP/6-31G(d) level. The valence orbital structure of boron buckyball is identical to the one in the carbon analogue.Comment: 10 pages, 1 Table, 2 Figure