Position-dependent-mass; Cylindrical coordinates, separability, exact solvability, and PT-symmetry

The kinetic energy operator with position-dependent-mass in cylindrical coordinates is obtained. The separability of the corresponding Schr\"odinger equation is discussed within radial cylindrical mass settings. Azimuthal symmetry is assumed and spectral signatures of various z-dependent interaction potentials (Hermitian and non-Hermitian PT-symmetric) are reported.Comment: 16 page

Gamma flashes from relativistic electron-positron plasma droplets

Ultra-intense lasers are expected to produce, in near future, relativistic electron-positron plasma droplets. Considering the local photon production rate in complete leading order in quantum electrodynamics (QED), we point out that these droplets are interesting sources of gamma ray flashesComment: 4 pages, 6 figures; Text has been revised and new refs. are adde

The neonatal splice variant of Nav1.5 potentiates in vitro invasive behaviour of MDA-MB-231 human breast cancer cells

Upregulation of functional voltage-gated Na+ channels (VGSCs) occurs in metastatic human breast cancer (BCa) in vitro and in vivo. The present study aimed to ascertain the specific involvement of the 'neonatal' splice variant of Nav1.5 (nNav1.5), thought to be predominant, in the VGSC-dependent invasive behaviour of MDA-MB-231 cells. Functional activity of nNav1.5 was suppressed by two different methods targeting nNav1.5: (i) small interfering RNA (siRNA), and (ii) a polyclonal antibody (NESO-pAb); effects upon migration and invasion were determined. nNav1.5 mRNA, protein and signalling were measured using real-time PCR, Western blotting, and patch clamp recording, respectively. Treatment with the siRNA rapidly reduced (by similar to 90%) the level of nNav1.5 (but not adult Nav1.5) mRNA, but the protein reduction was much smaller (similar to 30%), even after 13 days. Nevertheless, the siRNA reduced peak VGSC current density by 33%, and significantly increased the cells' sensitivity to nanomolar tetrodotoxin (TTX). Importantly, the siRNA suppressed in vitro migration by 43%, and eliminated the normally inhibitory effect of TTX. Migrated MDA-MB-231 cells expressed more nNav1.5 protein at the plasma membrane than non-migrated cells. Furthermore, NESO-pAb reduced migration by up to 42%, in a dose-dependent manner. NESO-pAb also reduced Matrigel invasion without affecting proliferation. TTX had no effect on cells already treated with NESO-pAb. It was concluded that nNav1.5 is primarily responsible for the VGSC-dependent enhancement of invasive behaviour in MDA-MB-231 cells. Accordingly, targeting nNav1.5 expression/activity may be useful in clinical management of metastatic BCa

Part of the D - dimensional Spiked harmonic oscillator spectra

The pseudoperturbative shifted - l expansion technique PSLET [5,20] is generalized for states with arbitrary number of nodal zeros. Interdimensional degeneracies, emerging from the isomorphism between angular momentum and dimensionality of the central force Schrodinger equation, are used to construct part of the D - dimensional spiked harmonic oscillator bound - states. PSLET results are found to compare excellenly with those from direct numerical integration and generalized variational methods [1,2].Comment: Latex file, 20 pages, to appear in J. Phys. A: Math. & Ge

Bound - states for truncated Coulomb potentials

The pseudoperturbative shifted - $l$ expansion technique PSLET is generalized for states with arbitrary number of nodal zeros. Bound- states energy eigenvalues for two truncated coulombic potentials are calculated using PSLET. In contrast with shifted large-N expansion technique, PSLET results compare excellently with those from direct numerical integration.Comment: TEX file, 22 pages. To appear in J. Phys. A: Math. & Ge

d-Dimensional generalization of the point canonical transformation for a quantum particle with position-dependent mass

The d-dimensional generalization of the point canonical transformation for a quantum particle endowed with a position-dependent mass in Schrodinger equation is described. Illustrative examples including; the harmonic oscillator, Coulomb, spiked harmonic, Kratzer, Morse oscillator, Poschl-Teller and Hulthen potentials are used as reference potentials to obtain exact energy eigenvalues and eigenfunctions for target potentials at different position-dependent mass settings.Comment: 14 pages, no figures, to appear in J. Phys. A: Math. Ge