On the quantisation of the angular momentum

When a hydrogen-like atom is treated as a two dimensional system whose configuration space is multiply connected, then in order to obtain the same energy spectrum as in the Bohr model the angular momentum must be half-integral.Comment: Latex, 5 page

Quantum Zeno Effect and Light-Dark Periods for a Single Atom

The quantum Zeno effect (QZE) predicts a slow-down of the time development of a system under rapidly repeated ideal measurements, and experimentally this was tested for an ensemble of atoms using short laser pulses for non-selective state measurements. Here we consider such pulses for selective measurements on a single system. Each probe pulse will cause a burst of fluorescence or no fluorescence. If the probe pulses were strictly ideal measurements, the QZE would predict periods of fluorescence bursts alternating with periods of no fluorescence (light and dark periods) which would become longer and longer with increasing frequency of the measurements. The non-ideal character of the measurements is taken into account by incorporating the laser pulses in the interaction, and this is used to determine the corrections to the ideal case. In the limit, when the time between the laser pulses goes to zero, no freezing occurs but instead we show convergence to the familiar macroscopic light and dark periods of the continuously driven Dehmelt system. An experiment of this type should be feasible for a single atom or ion in a trapComment: 16 pages, LaTeX, a4.sty; to appear in J. Phys.

Progress in Classical and Quantum Variational Principles

We review the development and practical uses of a generalized Maupertuis least action principle in classical mechanics, in which the action is varied under the constraint of fixed mean energy for the trial trajectory. The original Maupertuis (Euler-Lagrange) principle constrains the energy at every point along the trajectory. The generalized Maupertuis principle is equivalent to Hamilton's principle. Reciprocal principles are also derived for both the generalized Maupertuis and the Hamilton principles. The Reciprocal Maupertuis Principle is the classical limit of Schr\"{o}dinger's variational principle of wave mechanics, and is also very useful to solve practical problems in both classical and semiclassical mechanics, in complete analogy with the quantum Rayleigh-Ritz method. Classical, semiclassical and quantum variational calculations are carried out for a number of systems, and the results are compared. Pedagogical as well as research problems are used as examples, which include nonconservative as well as relativistic systems

From least action in electrodynamics to magnetomechanical energy -- a review

The equations of motion for electromechanical systems are traced back to the fundamental Lagrangian of particles and electromagnetic fields, via the Darwin Lagrangian. When dissipative forces can be neglected the systems are conservative and one can study them in a Hamiltonian formalism. The central concepts of generalized capacitance and inductance coefficients are introduced and explained. The problem of gauge independence of self-inductance is considered. Our main interest is in magnetomechanics, i.e. the study of systems where there is exchange between mechanical and magnetic energy. This throws light on the concept of magnetic energy, which according to the literature has confusing and peculiar properties. We apply the theory to a few simple examples: the extension of a circular current loop, the force between parallel wires, interacting circular current loops, and the rail gun. These show that the Hamiltonian, phase space, form of magnetic energy has the usual property that an equilibrium configuration corresponds to an energy minimum.Comment: 29 pages, 9 figures, 65 reference

From one version to the other. Intra-theoretical change

Describing scientific change involves displaying scientific theories and their content. This is done by way of (rational) reconstructions, which usually neglect the variety of versions in which a scientific theory may appear. Although they possess a unity allowing them to bear the same name for decades, or even centuries, theories are diachronic, evolving entities. How should their evolution, i.e., into-theoretical change, be described? I claim that this description is best done in terms of a series of conceptual undertakings on the part of scientists aiming at examining the meaning of theoretical principles and concepts and broadening their domain. I present the implications of this hypothesis, which follows Robert Brandom's views on the philosophy of language, as well as the conception of scientific change in general associated with it