Calculation of the energy spectrum of a two-electron spherical quantum dot

We study the energy spectrum of the two-electron spherical parabolic quantum dot using the exact Schroedinger, the Hartree-Fock, and the Kohn-Sham equations. The results obtained by applying the shifted-1/N method are compared with those obtained by using an accurate numerical technique, showing that the relative error is reasonably small, although the first method consistently underestimates the correct values. The approximate ground-state Hartree-Fock and local-density Kohn-Sham energies, estimated using the shifted-1/N method, are compared with accurate numerical self-consistent solutions. We make some perturbative analyses of the exact energy in terms of the confinement strength, and we propose some interpolation formulae. Similar analysis is made for both mean-field approximations and interpolation formulae are also proposed for these exchange-only ground-state cases.Comment: 18 pages, LaTeX, 2 figures-ep

Solution of Massless Spin One Wave Equation in Robertson-Walker Space-time

We generalize the quantum spinor wave equation for photon into the curved space-time and discuss the solutions of this equation in Robertson-Walker space-time and compare them with the solution of the Maxwell equations in the same space-time.Comment: 16 Pages, Latex, no figures, An expanded version of paper published in International Journal of Modern Physics A, 17 (2002) 113

Sub-Doppler resonances in the back-scattered light from random porous media infused with Rb vapor

We report on the observation of sub-Doppler resonances on the back-scattered light from a random porous glass medium with rubidium vapor filling its interstices. The sub-Doppler spectral lines are the consequence of saturated absorption where the incident laser beam saturates the atomic medium and the back-scattered light probes it. Some specificities of the observed spectra reflect the transient atomic evolution under confinement inside the pores. Simplicity, robustness and potential miniaturization are appealing features of this system as a spectroscopic reference.Comment: 6 pages, 4 figure

Bound states of scalar particles in the presence of a short range potential

We analyze the behavior of the energy spectrum of the Klein-Gordon equation in the presence of a truncated hyperbolic tangent potential. From our analysis we obtain that, for some values of the potential there is embedding of the bound states into the negative energy continuum, showing that, in opposition to the general belief, relativistic scalar particles in one-dimensional short range potentials can exhibit resonant behavior and not only the Schiff-Snyder effect.Comment: To appear in Modern Physics Letters

Editorial: Phosphoinositides and their phosphatases: Linking electrical and chemical signals in biological processes

The voltage-sensing phosphatase (VSP) has changed the way we think about both cellular electrical activity and PIPs (phosphatidylinositol phosphates). Originally discovered in 1999 (Chen et al., 1999), these proteins were not recognized as electrically-controlled enzymes until 2005 (Murata et al., 2005). They constitute the first, and so far the only, example of an enzyme linking electrical signals at the plasma membrane to the catalysis of PIPs (Murata et al., 2005), a ubiquitous family of intracellular signaling molecules (Di Paolo and De Camilli, 2006; Balla, 2013). Before the discovery of VSP, there were no known direct links between the two. Textbook examples would represent this connection with arrows, alluding to indirect or “yet-to-be-defined” signaling pathways. Now we know that VSP serves as a direct connection between the electrical nature of the cell and PIPs, lipid second messengers that are critical for cell survival. However, many questions remain unanswered regarding VSP and its electrical regulation of cellular processes. With the discovery of VSP, the membrane potential must now be considered when studying PIP regulators. PIPs are involved in almost all aspects of cell physiology from survival, proliferation, and migration to pre-programed cell death (Di Paolo and De Camilli, 2006; Logothetis et al., 2010; Koch and Holt, 2012; Balla, 2013). For example, PIP concentrations are actively polarized in migrating cells with phosphatidylinositol-3,4,5-trisphosphate (PI(3,4,5)P3) on the leading edge and phosphatidylinositol-4,5-bisphosphate (PI(4,5)P2) on the lagging edge (Leslie et al., 2008). These gradients in the concentration of PIPs are necessary for activation of Rac and Rho leading to cell motion. PIPs are also crucial for cell growth: PI(3,4,5)P3 activates the mTor cascade leading to increased protein, membrane, and nucleic acid production (Dibble and Manning,2013). Many human diseases have been associated with altered homeostasis of PIPs, including cancer, developmental disorders, and Alzheimer\u27s disease (Simpson and Parsons, 2001; McCrea and De Camilli, 2009; Hakim et al., 2012). Though the physiological relevance of VSP is not yet defined, it is still crucial to human health to understand how PIPs are regulated and that now includes VSP. All cells have an asymmetric composition of ions across their plasma membrane, which, combined with selective permeabilities for these ions, results in a difference in the electrical potential across their plasma membrane. This difference, called the membrane potential, constitutes a form of cell signaling and a source of energy, both driving many biological processes. This electrical potential difference powers neuronal excitability as well as more general processes like proliferation, migration, and development (Levin, 2007; Sundelacruz et al., 2009; Yao et al., 2011). Regulation by the membrane potential has long been the sole purview of ion channels and transporters and that has influenced what questions are asked regarding the changing potential. With our new knowledge of VSP, the changing membrane potential can directly signal the cell by modulating mTor and cell growth pathways, leading to abnormal growth or the M-current in sympathetic ganglion, leading to hyperexcitability. The articles in this Special Topic highlight several features of VSP including its unique activation, its similarities to other enzymes and its use as a versatile tool to study other proteins. In the review article by Hobiger and Friedrich (2015, p. 20), the authors compare the structural similarities and differences between the broader family of protein tyrosine phosphatases and one of its newest members, VSP. They suggest a catalytic mechanism based on this comparison. Castle et al. (2015, p. 63) investigate the activation mechanism of VSP by probing the C2 domain, the C-terminal domain of VSP that has been largely unrecognized before the recent crystal structures showed a direct contribution of the C2 residue Y522 into the active site. The work by Mavrantoni et al. (2015, p. 68) explores the techniques that are used to test VSP and address some of their limitations including the need for expensive electrophysiology equipment as well as the limitations of using channels as functional reporters. They take their methods and apply them to a chimera between the Ciona intestinalis VSP and human PTEN and show how the chimera allows for the investigation of PTEN using standard techniques but with the advantage of regulated activation, voltage. Beyond the molecular mechanism underlying VSP activity, Mori et al. (2015, p. 22) review the use of VSP as a relatively simple tool for manipulating PI(4,5)P2 concentrations in cells. They have used VSP to study the PI(4,5)P2 regulation of transient receptor potential canonical channels involved in receptor-operated calcium currents. Along the same lines, Rjasanow et al. (2015, p. 127) use VSP as a tool that gives them precise control over the PI(4,5)P2 concentrations in the membrane. These authors compared the relative PIP affinities between several ion channels. They also point out an important limitation that the channels must already have a known specificity for a particular PIP because VSP does not destroy PIPs in contrast to phospholipase C; instead, it generates multiple PIPs. All together, these articles underscore the features of VSP and expand our understanding of its function and utility. Though VSP remains relatively unknown to many, this nascent field has shown fast initial growth. The unique nature of these enzymes has inspired many to investigate their properties as well as take advantage of them. Many questions remain unanswered regarding VSP such as how the voltage sensor couples to the enzyme and whether the phosphatase domain is brought to the membrane for activation or whether a conformational change within the active site determines activation. We look forward to the studies that will address these and the many other questions that persist in this exciting field

Scattering of a Klein-Gordon particle by a Woods-Saxon potential

We solve the Klein-Gordon equation in the presence of a spatially one-dimensional Woods-Saxon potential. The scattering solutions are obtained in terms of hypergeometric functions and the condition for the existence of transmission resonances is derived. It is shown how the zero-reflection condition depends on the shape of the potential.Comment: 10 pages, Revtex. To appear in Phys. Rev.

Spectrum of the Relativistic Particles in Various Potentials

We extend the notion of Dirac oscillator in two dimensions, to construct a set of potentials. These potentials becomes exactly and quasi-exactly solvable potentials of non-relativistic quantum mechanics when they are transformed into a Schr\"{o}dinger-like equation. For the exactly solvable potentials, eigenvalues are calculated and eigenfunctions are given by confluent hypergeometric functions. It is shown that, our formulation also leads to the study of those potentials in the framework of the supersymmetric quantum mechanics

The Energy Eigenvalues of the Two Dimensional Hydrogen Atom in a Magnetic Field

In this paper, the energy eigenvalues of the two dimensional hydrogen atom are presented for the arbitrary Larmor frequencies by using the asymptotic iteration method. We first show the energy eigenvalues for the no magnetic field case analytically, and then we obtain the energy eigenvalues for the strong and weak magnetic field cases within an iterative approach for $n=2-10$ and $m=0-1$ states for several different arbitrary Larmor frequencies. The effect of the magnetic field on the energy eigenvalues is determined precisely. The results are in excellent agreement with the findings of the other methods and our method works for the cases where the others fail.Comment: 13 pages and 5 table