On the Hamilton-Jacobi equation for second class constrained systems

We discuss a general procedure for arriving at the Hamilton-Jacobi equation of second-class constrained systems, and illustrate it in terms of a number of examples by explicitely obtaining the respective Hamilton principal function, and verifying that it leads to the correct solution to the Euler-Lagrange equations.Comment: 17 pages, to appear in Ann. Phy

Using the National Benchmark Tests in Engineering diplomas: revisiting generic academic literacy

Proficiency tests are being used moreextensively at institutions of higher learningfor selection, placement, for diagnostic purposes and as a means of early identificationfor first year entering students who might be at risk of under-performance. Given thatat some institutions a high premium is placed on these test results, one of the issues atstake is the extent to which the generic test content relates to curriculum practices inthe various disciplines. This article focuses on three Engineering diplomas and exploresthe extent to which the test specifications of the National Benchmark Test in academicliteracy relate to reading and writing practices in the discipline. The contention is thatthere should be a relationship between the test specifications and academic literacypractices at first year level in order to provide the data necessary to appropriately placeand support students who might be at risk of under-performance.Keywords: national benchmark test; proficiency test; academic literacy; engineeringdiplom

Observation of Exceptional Points in Electronic Circuits

Two damped coupled oscillators have been used to demonstrate the occurrence of exceptional points in a purely classical system. The implementation was achieved with electronic circuits in the kHz-range. The experimental results perfectly match the mathematical predictions at the exceptional point. A discussion about the universal occurrence of exceptional points -- connecting dissipation with spatial orientation -- concludes the paper.Comment: 4 pages, latex, 3 postscript figures, submitted for publicatio

Die afrikaner en sy pers*

Die versoek w at van u inrigting tot my gekom het om buitengewone professor in die Persw etenskap te word, was vir my deels vererend, m aar deels het dit my in 'n moeilike posisie gestel. Dit was vir my vererend, om dat dit gekom het van 'n universiteit m et wie se Christelik- Nasionale koers ek my ten voile kan vereenselwig. Dit was dan ook vir my vererend, om dat ek daardeur in staat gestel kan w ord om die volk w aartoe ek behoort, op 'n vir my nuwe terrein te dien. As sodanig is dit vir my im m ers m oontlik om ook ’n beskeie bydrae te lewer tot die geestelike vorm ing van die jeug van ons volk. Dit het my m oeilik geval om, w aar ek reeds die m iddeljarige leeftyd bereik het, nou vir die eerste maal as dosent op te tree, aangesien ek daarvan in die verlede nie die m inste kennis en ervaring opgedoen het nie. As joernalis rig ek my im m ers tot die breë publiek deur middel van die pen. As dosent m oet ek my deur middel van die mond tot die studente rig. Dit lê voor die hand dat die eise w at so aan my gestel word, totaal anders is as dié waar- aan ek oor 'n tydperk van m eer as 'n kw arteeu as joer­ nalis gewoond geraak het

Spectrum of the non-commutative spherical well

We give precise meaning to piecewise constant potentials in non-commutative quantum mechanics. In particular we discuss the infinite and finite non-commutative spherical well in two dimensions. Using this, bound-states and scattering can be discussed unambiguously. Here we focus on the infinite well and solve for the eigenvalues and eigenfunctions. We find that time reversal symmetry is broken by the non-commutativity. We show that in the commutative and thermodynamic limits the eigenstates and eigenfunctions of the commutative spherical well are recovered and time reversal symmetry is restored

Twist Deformation of Rotationally Invariant Quantum Mechanics

Non-commutative Quantum Mechanics in 3D is investigated in the framework of the abelian Drinfeld twist which deforms a given Hopf algebra while preserving its Hopf algebra structure. Composite operators (of coordinates and momenta) entering the Hamiltonian have to be reinterpreted as primitive elements of a dynamical Lie algebra which could be either finite (for the harmonic oscillator) or infinite (in the general case). The deformed brackets of the deformed angular momenta close the so(3) algebra. On the other hand, undeformed rotationally invariant operators can become, under deformation, anomalous (the anomaly vanishes when the deformation parameter goes to zero). The deformed operators, Taylor-expanded in the deformation parameter, can be selected to minimize the anomaly. We present the deformations (and their anomalies) of undeformed rotationally-invariant operators corresponding to the harmonic oscillator (quadratic potential), the anharmonic oscillator (quartic potential) and the Coulomb potential.Comment: 20 page

Variations on the Planar Landau Problem: Canonical Transformations, A Purely Linear Potential and the Half-Plane

The ordinary Landau problem of a charged particle in a plane subjected to a perpendicular homogeneous and static magnetic field is reconsidered from different points of view. The role of phase space canonical transformations and their relation to a choice of gauge in the solution of the problem is addressed. The Landau problem is then extended to different contexts, in particular the singular situation of a purely linear potential term being added as an interaction, for which a complete purely algebraic solution is presented. This solution is then exploited to solve this same singular Landau problem in the half-plane, with as motivation the potential relevance of such a geometry for quantum Hall measurements in the presence of an electric field or a gravitational quantum well