Table of contents

Isomorphism of finite molecular point groups has been examined in an exhaustive and systematic way. Several molecular abstract groups are derived and a new definition of isosymmetric molecules proposed, based on the notion of abstract group. The information is summarized in the 'periodic table' of molecular symmetries.

The electromagnetic force exerted between two oppositely charged and moving particles is not reduced to the Coulombian attraction: there are also, not counting radiation damping, the Darwin corrections. Perturbations due to this fact are studied, over a time where the effects of the radiation damping are negligible. Their effect is a rotation of the elliptic trajectories, the same than this due to the relativistic variation of a moving mass, but with the reduced mass!.

We shall demonstrate how to carry out the Hamiltonian description of a particle only subject to apparent forces. We shall see that such a system exhibits gauge invariance properties and that it may be described within the framework of the Dirac constraint theory. Finally, we shall examine the inherent process of quantization.

I discuss some of the didactic problems in the introduction to quantum physics based on the concept of photon. I specifically argue that the derivation of the photon energy from the relativistic Doppler shift offers stimulating didactic opportunities. A detailed form of this derivation reveals the subtle link between relativity and quantization, and also helps in elucidating the meaning of the invariance of the speed of light.

We investigate the dynamics of toast tumbling from a table to the floor. Popular opinion is that the final state is usually butter-side down, and constitutes prima facie evidence of Murphy's Law ('If it can go wrong, it will'). The orthodox view, in contrast, is that the phenomenon is essentially random, with a 50/50 split of possible outcomes. We show that toast does indeed have an inherent tendency to land butter-side down for a wide range of conditions. Furthermore, we show that this outcome is ultimately ascribable to the values of the fundamental constants. As such, this manifestation of Murphy's Law appears to be an ineluctable feature of our universe.

Thermodynamic equilibrium between linear phases separated by point phases is not possible. A new general proof is presented based on an analysis of the Omega -potential of a heterogeneous linear system.

We extend the treatment of translation symmetry, which is usually limited to orbitals (one-electron functions), to many-electron functions. The distinction between translational invariance and translation symmetry is analysed. We define an explicit translation operator for many-electron functions. The many-electron translation operators are related to the many-electron momentum operator, of which several forms are discussed.

In this paper the usual procedure, which consists of dislocating the barrel with respect to the rest of the instrument to improve the tuning of a clarinet, is analysed regarding consequences to the tone quality.

We review the idea of the generation of time-dependent elemental dipoles in a material medium due to a point charge moving with constant velocity inside it. We obtain that if the velocity of the point charge is greater than the velocity of light in such medium, that is nu >c/ square root epsilon , there is a coherent superposition of the radiation emitted by each elemental dipole; we identify the total coherent radiation as the Cherenkov radiation.

A general Heisenberg exchange effective Hamiltonian is deduced in a straightforward way from the elemental quantum mechanical principles for the case of magnetic ions with non-orbital degeneracy in a crystalline lattice. Expressions for the high order direct exchange coupling constants or parameters are presented. The meaning of this effective Hamiltonian is important because extracting information from the Heisenberg Hamiltonian is a difficult task and is however taken as the starting point for many quite profound investigations of magnetism in solids and therefore could play an important role in an introductory course to solid state physics.

The concept of magnetic stresses as transmitters of magnetic forces is revisited with the aim of showing that it can facilitate calculations and the understanding of magnetic interaction at an undergraduate level. A simple derivation of magnetic stresses in vacuum and magnetized plasmas is presented. As an illustrative example magnetic stresses are used to calculate the forces between parallel conductors.