Classical and Quantum Behavior of Generalized Oscillators in Terms of Linear Canonical Transformations

The quantum mechanical relationships between time-dependent oscillators, Hamilton-Jacobi theory and an invariant operator are clarified by making reference to a system with a generalized oscillator. We introduce a linear transformation in position and momentum, and show that the correspondence between classical and quantum transformations is exactly one-to-one. We found that classical canonical transformations are constructed from quantum unitary transformations as long as we are concerned with linear transformations. We also show the relationship between the invariant operator and a linear transformation.

Vibronic effect study of ^(1)A_(2) state of H_(2)O and D_(2)O

The generalized oscillator strengths of the dipole-forbidden excitations of the ^(1)A_(2) of H_(2)O and D_(2)O were calculated with the time dependent density functional theory,by taking into account the vibronic effect.It is found that the vibronic effect converts the dipole-forbidden excitation of the ^(1)A_(2) into a dipole-allowed one,which enhances the intensities of the corresponding generalized oscillator strength in the small squared momentum transfer region.The present investigation shows that the vibronic effect of H_(2)O is slightly stronger than that of D_(2)O,which exhibits a clear isotopic effect.

Exact solution of the generalized Kemmer oscillator

In the present work, the generalized Kemmer oscillator was introduced in one dimension. It is shown that the exact solutions of generalized Kemmer oscillator with some appropriate choices of the interactions f（x） have been obtained by using the Nikiforov-Uvarov （NU） method. Moreover, several interesting cases are discussed.

Generalized oscillator strengths for some higher valence-shell excitations of krypton atom

The valence-shell excitations of krypton atom have been investigated by fast electron impact with an angle-resolved electron-energy-loss spectrometer. The generalized oscillator strengths for some higher mixed valence-shell excitations in 4d, 4f, 5p, 5d, 6s, 6p, 7s ←4p of krypton atom have been determined. Their profiles are discussed, and the generalized oscillator strengths for the electric monopole and quadrupole excitations in 5p ← 4p are compared with the calculations of Amusia et al. （Phys. Rev. A 67 022703 （2003））. The differences between the experimental results and theoretical calculations show that more studies are needed.

Generalized Harmonic Oscillator and the Schrdinger Equation with Position-Dependent Mass

We study the generalized harmonic oscillator that has both the position-dependent mass and the potential depending on the form of mass function in a more general framework. The explicit expressions of the eigenvalue and eigenfunction for such a system are given, they have the same forms as those for the usual harmonic oscillator with constant mass. The coherent state and its properties corresponding effective potentials for several mass functions, for the system with PDM are also discussed. We give the the systems with such potentials are isospectral to the usual harmonic oscillator.

Exact solution of the (1+2)-dimensional generalized Kemmer oscillator in the cosmic string background with the magnetic field

We study a two-dimensional generalized Kemmer oscillator in the cosmic string spacetime with the magnetic field to better understand the contribution from gravitational field caused by topology defects,and present the exact solutions to the generalized Kemmer equation in the cosmic string with the Morse potential and Coulomb-liked potential through using the Nikiforov-Uvarov(NU)method and biconfluent Heun equation method,respectively.Our results give the topological defect’s correction for the wave function,energy spectrum and motion equation,and show that the energy levels of the generalized Kemmer oscillator rely on the angular deficitαconnected with the linear mass density m of the cosmic string and characterized the metric’s structure in the cosmic string spacetime.

N = 4 Supersymmetric Morse Oscillator and Its Spectrum-Generating Algebra

In this paper N = 4 supersymmetry of generalized Morse oscillators in one dimension is studied. Both bound states and scattering states of its four superpartner Hamiltonians are analyzed by using unitary irreducible representations of the noncompact Lie algebra su(1,1). The spectrum-generating algebra governing the Hamiltonian of the N = 4 supersymmetric Morse oscillator is shown to be connected with the realization of Lie superalgebra osp(1,2)or B(0,1) in terms of the variables of a supersymmetric two-dimensional harmonic oscillator.

On precise time integration method for non-classically damped MDOF systems

In the complex mode superposition method, the equations of motion for non-classically damped multiple-degree-of-freedom （MDOF） discrete systems can be transferred into a combination of some generalized SDOF complex oscillators. Based on the state space theory, a precise recurrence relationship for these complex oscillators is set up; then a delicate general solution of non-classically damped MDOF systems, completely in real value form, is presented in this paper. In the proposed method, no calculation of the matrix exponential function is needed and the algorithm is unconditionally stable. A numerical example is given to demonstrate the validity and efficiency of the proposed method.

Boundedness of Solutions of Nonlinear Systems of Differential Equations

We first give an example to illustrate that the results in [12] concerning the boundedness of solutions of nonlinear oscillatory equations are not true. And then we obtain sufficient or necessary conditions for the boundedness of solutions of the nonlinear system of differential equations dx/dt=y~α, dy/dt=-f(x)y~βh(y)-g(x)k(y) without the usual signum conditions xg(x)】0 for all x≠0 and f(x)≥0 for all x∈R.

High voltage generator circuit with low power and high efficiency applied in EEPROM

This paper presents a low power and high efficiency high voltage generator circuit embedded in electrically erasable programmable read-only memory（EEPROM）.The low power is minimized by a capacitance divider circuit and a regulator circuit using the controlling clock switch technique.The high efficiency is dependent on the zero threshold voltage（V_（th）） MOSFET and the charge transfer switch（CTS） charge pump.The proposed high voltage generator circuit has been implemented in a 0.35μm EEPROM CMOS process.Measured results show that the proposed high voltage generator circuit has a low power consumption of about 150.48μW and a higher pumping efficiency（83.3%） than previously reported circuits.This high voltage generator circuit can also be widely used in low-power flash devices due to its high efficiency and low power dissipation.