Evading Quantum Mechanics \'{a} la Sudarshan: quantum-mechanics-free subsystem as a realization of Koopman-von Neumann mechanics

Tsang and Caves suggested the idea of a quantum-mechanics-free subsystem in 2012. We contend that Sudarshan's viewpoint on Koopman-von Neumann mechanics is realized in the quantum-mechanics-free subsystem. Since quantum-mechanics-free subsystems are being experimentally realized, Koopman-von Neumann mechanics is essentially transformed into an engineering science.Comment: 5 pages, no figure

Two-photon decay of P-wave positronium: a tutorial

A detailed exposition of two-photon decays of P-wave positronium is given to fill an existing gap in the pedagogical literature. Annihilation decay rates of P-wave positronium are negligible compared to the rates of radiative electric dipole transitions to the ground state. This circumstance makes such decays experimentally inaccessible. However the situation is different for quarkonium and the experimental and theoretical research of two-photon and two-gluon decays of P-wave quarkonia is a still flourishing field.Comment: 12 pages, 1 figure, to be published in Can. J. Phy

Majorana transformation of the Thomas-Fermi equation demystified

The Majorana transformation makes it possible to reduce the Thomas-Fermi equation to a first-order differential equation. This reduction is possible due to the special scaling property of the Thomas-Fermi equation under homology transformations. Such reductions are well known in the context of stellar astrophysics, where the use of homology-invariant variables has long proved useful. We use homology-invariant variables in the context of the Thomas-Fermi equation to demystify the origin of the otherwise mysterious Majorana transformation.Comment: 10 pages, no figure

Hourglass of constant weight as an illustrative example of a system with a variable mass

We provide an alternative approach to a problem posed in the article "Hourglass of Constant Weight" by Volker Becker and Thorsten P\"{o}schel, which appeared in Granular Matter 10 (2008), 231-232, i.e. 14 years ago. Our goal to return to this article after so much time is purely pedagogical. Although there is a slight and subtle inaccuracy in the derivation of equation (8) in the work of Becker and P\"{o}schel, which we correct, we use this circumstance only to give a detailed pedagogical exposition of an excellent physical problem and to show the pedagogical usefulness of the concept of momentum flux when considering the mechanics of systems with variable mass.Comment: 14 pages, 3 figures, to be published in Granular Matte

Berry phase of spin-one system in a rotating electric field

We consider in sufficient detail how the Berry phase arises in a rotating electric field in a model system with spin one. The goal is to help the student who first encountered this interesting problem, which is fraught with some subtleties that require attention in order not to go astray.Comment: 10 pages, no figure