Exact Wave Functions for Generalized Harmonic Oscillators

We transform the time-dependent Schroedinger equation for the most general variable quadratic Hamiltonians into a standard autonomous form. As a result, the time-evolution of exact wave functions of generalized harmonic oscillators is determined in terms of solutions of certain Ermakov and Riccati-type systems. In addition, we show that the classical Arnold transformation is naturally connected with Ehrenfest's theorem for generalized harmonic oscillators.Comment: 10 pages, no figure

Academic Support at Leeds Metropolitan Library

Leeds Metropolitan’s Library Academic Support Stream is made up of Academic Librarians and Information Services Librarians who provide academic support to the university’s six faculties. The team use innovative methods of working together to engage students and enhance their experience. The team only formed a year ago so this is a good time to reflect on our success so far. The library service at Leeds Met is continually developing and offers new challenges and opportunities for staff providing library academic support. Innovation has even become part of our new name – ‘Libraries and Learning Innovation’. We still offer all the traditions types of library academic support, but there is an increasing emphasis on finding innovative ways of supporting students and publicising what we can offer. This year the Library Academic Support Stream won a University Attitude Character and Talents Award for Future Focus

The Role of the Pauli-Lubanski Vector for the Dirac, Weyl, Proca, Maxwell, and Fierz-Pauli Equations

We analyze basic relativistic wave equations for the classical fields, such as Dirac's equation, Weyl's two-component equation for massless neutrinos, and the Proca, Maxwell, and Fierz-Pauli equations, from the viewpoint of the Pauli-Lubanski vector and the Casimir operators of the Poincare group. In general, in this group-theoretical approach, the above wave equations arise in certain overdetermined forms, which can be reduced to the conventional ones by a Gaussian elimination. A connection between the spin of a particle/field and consistency of the corresponding overdetermined system is emphasized in the massless case.Comment: 27 pages, no figures, 1 table, 73 reference

Diversification and the rate of molecular evolution: no evidence of a link in mammals

BACKGROUND Recent research has indicated a positive association between rates of molecular evolution and diversification in a number of taxa. However debate continues concerning the universality and cause of this relationship. Here, we present the first systematic investigation of this relationship within the mammals. We use phylogenetically independent sister-pair comparisons to test for a relationship between substitution rates and clade size at a number of taxonomic levels. Total, non-synonymous and synonymous substitution rates were estimated from mitochondrial and nuclear DNA sequences. RESULTS We found no evidence for an association between clade size and substitution rates in mammals, for either the nuclear or the mitochondrial sequences. We found significant associations between body size and substitution rates, as previously reported. CONCLUSIONS Our results present a contrast to previous research, which has reported significant positive associations between substitution rates and diversification for birds, angiosperms and reptiles. There are three possible reasons for the differences between the observed results in mammals versus other clades. First, there may be no link between substitution rates and diversification in mammals. Second, this link may exist, but may be much weaker in mammals than in other clades. Third, the link between substitution rates and diversification may exist in mammals, but may be confounded by other variables