Relativity of representations in quantum mechanics

Only the position representation is used in introductory quantum mechanics and the momentum representation is not usually presented until advanced undergraduate courses. To emphasize the relativity of the representations of the abstract formulation of quantum mechanics, two examples of representations related to the operators aX+(1-a)P and (XP+PX)/2 are presented.Comment: 10 pages, no figures, accepted in Am.J.Phy

Quantum mechanics in finite dimensional Hilbert space

The quantum mechanical formalism for position and momentum of a particle in a one dimensional cyclic lattice is constructively developed. Some mathematical features characteristic of the finite dimensional Hilbert space are compared with the infinite dimensional case. The construction of an unbiased basis for state determination is discussed.Comment: 14 pages, no figure

A search for Galactic transients disguised as gamma-ray bursts

A significant fraction of cosmological gamma-ray bursts (GRBs) are characterised by a fast rise and exponential decay (FRED) temporal structure. This is not a distinctive feature of this class, since it is observed in many Galactic transients and is likely descriptive of a sudden release of energy followed by a diffusion process. Possible evidence has recently been reported by Tello et al. (2012) for a Galactic contamination in the sample of FRED GRBs discovered with Swift. We searched for possible Galactic intruders disguised as FRED GRBs in the Swift catalogue up to September 2014. We selected 181 FRED GRBs (2/3 with unknown redshift) and considered different subsamples. We tested the degree of isotropy through the dipole and the quadrupole moment distributions, both with reference to the Galaxy and in a coordinate-system-independent way, as well as with the two-point angular autocovariance function. In addition, we searched for possible indicators of a Galactic origin among the spectral and temporal properties of individual GRBs. We found marginal (~3 sigma) evidence for an excess of FREDs with unknown redshift towards the Galactic plane compared with what is expected for an isotropic distribution corrected for the non-uniform sky exposure. However, when we account for the observational bias against optical follow-up observations of low-Galactic latitude GRBs, the evidence for anisotropy decreases to ~2 sigma. In addition, we found no statistical evidence for different spectral or temporal properties from the bulk of cosmological GRBs. We found marginal evidence for the presence of a disguised Galactic population among Swift GRBs with unknown redshift. The estimated fraction is f=(19 +- 11)%, with an upper limit of 34% (90% confidence).Comment: 6 pages, 4 figures, accepted by A&