Energy measurements play a fundamental role in the theory of quantum mechanics, yet there is evidence that the underlying concepts are difficult for many students, even after all undergraduate instruction. We present results from an investigation into student ability to determine the possible energies that can be measured for a given wave function…

Franck-Condon factors (FCFs) play a crucial role in determining the intensities of the vibrational bands in electronic transitions. In this article, a relatively simple method to calculate the FCFs is illustrated. An algorithm for the Fourier Grid Hamiltonian (FGH) method for computing the vibrational wave functions and the corresponding energy…

Some peculiarities of the heat transfer through a sample that is heated by the superficial absorption of light energy under continuous uniform illumination are discussed. We explain, using a different approach to that presented in a recent article published in this journal (Salazar "et al" 2010 "Eur. J. Phys." 31 1053-9), that the front surface of…

The parametric oscillations of an oscillator driven electromagnetically are presented. The oscillator is a conductive pipe hung from a spring, and driven by the oscillating magnetic field of a surrounding coil in the presence of a static magnetic field. It is an interesting case of parametric oscillations since the pipe is neither a magnet nor a…

Dimensional analysis, superposition principle, and continuity of electric potential are used to study the electric potential of a uniformly charged square sheet on its plane. It is shown that knowing the electric potential on the diagonal and inside the square sheet is equivalent to knowing it everywhere on the plane of the square sheet. The…

We propose a simple and straightforward method based on Wronskians for the calculation of bound-state energies and wavefunctions of one-dimensional quantum-mechanical problems. We explicitly discuss the asymptotic behaviour of the wavefunction and show that the allowed energies make the divergent part vanish. As illustrative examples we consider…

The requirement of rotational invariance for lattice potential energies is investigated. Starting from this condition, it is shown that the Cauchy relations for the elastic constants are fulfilled if the lattice potential is built from pair interactions or when the first-neighbour approximation is adopted. This is seldom recognized in widely used…

A core topic in graduate courses in electrodynamics is the description of radiation from an accelerated charge and the associated radiation reaction. However, contemporary papers still express a diversity of views on the question of whether or not a uniformly accelerating charge radiates suggesting that a complete "physical" understanding of the…

This article discusses the development of beginning physics teachers' pedagogical content knowledge (PCK) in the context of teaching basic electricity during a one-year Professional Graduate Diploma in Education (PGDE) course and beyond. This longitudinal study used repeated semi-structured interviews over a period of four-and-a-half years. The…

The objective of this introduction to Colombeau algebras of generalized functions (in which distributions can be freely multiplied) is to explain in elementary terms the essential concepts necessary for their application to basic nonlinear problems in classical physics. Examples are given in hydrodynamics and electrodynamics. The problem of the…

We describe courses designed to help future teachers reflect on and discuss both physics content and student knowledge thereof. We use three kinds of activities: reading and discussing the literature, experiencing research-based curricular materials, and learning to use the basic research methods of physics education research. We present a general…

The laboratory (lab) frame angular distribution derived in two-body scattering theory exhibits a singularity at the maximum lab scattering angle. The singularity appears in the kinematic factor that transforms the centre of momentum (cm) angular distribution to the lab angular distribution. We show that it is caused in the transformation by the…

The recently observed acceleration of the expansion of the universe is a topic of intense interest. The favoured causes are the "cosmological constant" or "dark energy". The former, which appears in the Einstein equations as the term [lambda]g[subscript [mu]v], provides an extremely simple, well-defined mechanism for the acceleration. However,…

The covariant formulation of Maxwell's equations can be expressed in a form independent of the usual systems of units by introducing the constants alpha, beta and gamma into these equations. Maxwell's equations involving these constants are then specialized to the most commonly used systems of units: Gaussian, SI and Heaviside-Lorentz by giving…

In this paper, a procedure is presented that will allow (i) the power and (ii) the energy of a pulsed and tuneable TEA CO[subscript 2] laser to be optimized. This type of laser represents a significant improvement in performance and portability. Combining a pulse mode with a grating tuning facility, it enables us to scan the working wavelength…