Inverted Oscillator

The inverted harmonic oscillator problem is investigated quantum mechanically. The exact wave function for the confined inverted oscillator is obtained and it is shown that the associated energy eigenvalues are discrete and it is given as a linear function of the quantum number $n$.Comment: 4 page

Stability of an Exciton bound to an Ionized Donor in Quantum Dots

Total energy, binding energy, recombination rate (of the electron hole pair) for an exciton (X) bound in a parabolic two dimensional quantum dot by a donor impurity located on the z axis at a distance d from the dot plane, are calculated by using the Hartree formalism with a recently developed numerical method (PMM) for the solution of the Schroedinger equation. As our analysis indicates there is a critical dot radius such that for radius less than the critical radius the complex is unstable and with an increase of the impurity distance this critical radius increases. Furthermore, there is a critical value of the mass ratio such that for mass ratio less than the critical value the complex is stable. The appearance of this stability condition depends both on the impurity distance and the dot radius, in a way that with an increase of the impurity distance we have an increase in the maximum dot radius where this stability condition appears. For dot radii greater than this maximum dot radius (for fixed impurity distance) the complex is always stable.Comment: 17 pages, 7 figures Applying a new numerical method which is based on the adiabatic stability of quantum mechanics, we study the stability of an exciton (X) bound in a parabolic two dimensional quantum dot by a donor impurity located on the z axis at a distance d from the dot plan

On the construction of pseudo-hermitian quantum system with a pre-determined metric in the Hilbert space

A class of pseudo-hermitian quantum system with an explicit form of the positive-definite metric in the Hilbert space is presented. The general method involves a realization of the basic canonical commutation relations defining the quantum system in terms of operators those are hermitian with respect to a pre-determined positive definite metric in the Hilbert space. Appropriate combinations of these operators result in a large number of pseudo-hermitian quantum systems admitting entirely real spectra and unitary time evolution. The examples considered include simple harmonic oscillators with complex angular frequencies, Stark(Zeeman) effect with complex electric(magnetic) field, non-hermitian general quadratic form of N boson(fermion) operators, symmetric and asymmetric XXZ spin-chain in complex magnetic field, non-hermitian Haldane-Shastry spin-chain and Lipkin-Meshkov-Glick model.Comment: 29 pages, revtex, minor changes, version to appear in Journal of Physics A(v3

Quantum Tunneling in the Wigner Representation

Time dependence for barrier penetration is considered in the phase space. An asymptotic phase-space propagator for nonrelativistic scattering on a one - dimensional barrier is constructed. The propagator has a form universal for various initial state preparations and local potential barriers. It is manifestly causal and includes time-lag effects and quantum spreading. Specific features of quantum dynamics which disappear in the standard semi-classical approximation are revealed. The propagator may be applied to calculation of the final momentum and coordinate distributions, for particles transmitted through or reflected from the potential barrier, as well as for elucidating the tunneling time problem.Comment: 18 pages, LATEX, no figure

Facile green synthesis of magnesium oxide nanoparticles using tea (Camellia sinensis) extract for efficient photocatalytic degradation of methylene blue dye

Herein, we report, for the first time, the synthesis, characterization, and the photocatalytic methyl blue dye degradation performance of magnesium oxide (MgO) nanoparticles (NPs) synthesized by a facile green approach using Camellia sinensis (tea leaves) extract as a reducing agent. The as-prepared materials were characterized by x-ray diffraction (XRD), which confirmed the large-scale synthesis of well crystalline cubic crystalline phase MgO NPs. Rietveld refinement analysis of the XRD pattern was done to determine the crystallographic parameters of the MgO NPs and to investigate lattice defects. Microstrain, lattice stress and energy density were calculated using Williamson-Hall analysis The synthesized nanoparticles exhibited over 97% photocatalytic degradation efficiency of methylene blue (MB) dye. Complementary density functional theory (DFT) calculations revealed the favorable formation of O 2 − radicals on the MgO (001) surface as the drivers of the MB dye degradation

Binding energy of hydrogenic impurity states in an inverse parabolic quantum well under static external fields

68.65.Fg Quantum wells, 61.72.-y Defects and impurities in crystals; microstructure, 83.60.Np Effects of electric and magnetic fields,