About One-Dimensional Conservative Systems with Position Depending Mass

For a one-dimensional conservative system with position depending mass, one deduces consistently a constant of motion, a Lagrangian, and a Hamiltonian for the nonrelativistic case. With these functions, one shows the trajectories on the spaces (x,v) and (x,p) for a linear position depending mass. For the relativistic case, the Lagrangian and Hamiltonian cannot be given explicitly in general. However, we study the particular system with constant force and mass linear dependence on the position where the Lagrangian can be found explicitly, but the Hamiltonian remains implicit in the constant of motion.

Electrostatic-lenses position-sensitive TOF MCP detector for beam diagnostics and new scheme for mass measurements at HIAF

A foil–microchannel plate(MCP)detector,which uses electrostatic lenses and possesses both good position and timing resolutions,has been designed and simulated for beam diagnostics and mass measurements at the next-generation heavy-ion-beam facility HIAF in China.Characterized by low energy loss and good performances of timing and position measurements,it would be located at focal planes in fragment separator HFRS for position monitoring,beam turning,Bq measurement,and trajectory reconstruction.Moreover,it will benefit the building-up of a magnetic-rigidity–energy-loss–time-offlight(BqDETOF)method at HFRS for high-precision in-flight particle identification of radioactive isotope beams on an event-by-event basis.Most importantly,the detector can be utilized for in-ring TOF and position measurements,beam-line TOF measurements at two achromatic foci,and position measurements at a dispersive focus of HFRS,thus making it possible to use two complementary mass measurement methods[isochronous mass spectrometry at the storage ring SRing and magnetic-rigidity–time-of-flight(BqTOF)at the beam-line HFRS]in one single experimental run.

A New Class of Exactly Solvable Models within the Schrodinger Equation with Position Dependent Mass

The study of physical systems endowed with a position-dependent mass (PDM) remains a fundamental issue of quantum mechanics. In this paper we use a new approach, recently developed by us for building the quantum kinetic energy operator (KEO) within the Schrodinger equation, in order to construct a new class of exactly solvable models with a position varying mass, presenting a harmonic-oscillator-like spectrum. To do so we utilize the formalism of supersymmetric quantum mechanics (SUSY QM) along with the shape invariance condition. Recent outcomes of non-Hermitian quantum mechanics are also taken into account.

Bound State Solutions of Schrdinger Equation for Generalized Morse Potential with Position-Dependent Mass

The effective mass one-dimensional Schrdinger equation for the generalized Morse potential is solved by using Nikiforov-Uvarov method. Energy eigenvalues and corresponding eigenfunctions are computed analytically. The results are a/so reduced to the constant mass case. Energy eigenvalues are computed numerically for some diatomic molecules. They are in agreement with the ones obtained before.

Non-hypergeometric Type of Polynomials and Solutions of Schrodinger Equation with Position-Dependent Mass

Using the coordinate transformation method,we study the polynomial solutions of the Schrodinger equationwith position-dependent mass (PDM).The explicit expressions for the potentials,energy eigenvalues,and eigenfunctionsof the systems are given.The issues related to normalization of the wavefunctions and Hermiticity of the Hamiltonianare also analyzed.

IDENTIFICATION OF DOUBLE BOND POSITION IN HEXADECENYL ACETATES BY MASS SPECTROMETRY

A method for locating double bond in hexadecenyl acetates has been developed by analyzing the mass spectral patterns on a fuzzy classification. The procedure was tested with the spectra of Δ~2- to Δ^(15)-isomers and the original double-bond position in these acetates was located unambiguously.

Generation of Exactly Solvable Potentials of Position-Dependent Mass Schrödinger Equation from Hulthen Potential

Exactly Solvable Potentials (ESPs) of Position-Dependent Mass (PDM) Schrodinger equation are generated from Hulthen Potential (parent system) by using Extended Transformation (ET) method. The method includes a Co-ordinate Transformation (CT) followed by Functional Transformation (FT) of wave function. Mass function of parent system gets transformed to that of generated system. Two new ESPs are generated. The explicit expressions of mass functions, energy eigenvalues and corresponding wave functions for newly generated potentials (systems) are derived. System specific regrouping method is also discussed.

One Dimensional Conservative System with Quadratic Dissipation and Position Depending Mass

Forl a 1-D conservative system with a position depending mass within a dissipative medium, its effect on the body is to exert a force depending on the squared of its velocity, a constant of motion, Lagrangian, generalized linear momentum, and Hamiltonian are obtained. We apply these new results to the harmonic oscillator and pendulum under the characteristics mentioned about, obtaining their constant of motion, Lagrangian and Hamiltonian for the case when the body is increasing its mass.

Coherent States and Uncertainty Product of the Harmonic Oscillator with Position-Dependent Mass

In this work, we applied the invariant method to calculate the coherent state of the harmonic oscillator with position-dependent mass, which in modern physics has great application. We also obtain the calculation of Heisenberg’s uncertainty principle, and we will show that it is verified.

Generalized Harmonic Oscillator and the Schrdinger Equation with Position-Dependent Mass

我们学习有位置依赖者团和潜力在一个更一般的框架工作取决于质量的表格的概括泛音振荡器。为如此的一个系统的特征值和特徵函数的明确的表情被给，他们与经常的质量为平常的泛音振荡器有象那些的一样的表格。为有 PDM 的系统的协调状态和它的性质也被讨论。我们为几个集体函数给相应有效潜力，有如此的潜力的系统是到平常的泛音振荡器的 isospectral。

Bound states of the Dirac equation with position-dependent mass for the Eckart potential

Studying with the asymptotic iteration method, we present approximate solutions of the Dirac equation for the Eckart potential in the case of position-dependent mass. The centrifugal term is approximated by an exponential form, and the relativistic energy spectrum and the normalized eigenfunctions are obtained explicitly.

Shannon information entropies for position-dependent mass Schrdinger problem with a hyperbolic well

The Shannon information entropy for the Schrodinger equation with a nonuniform solitonic mass is evaluated for a hyperbolic-type potential. The number of nodes of the wave functions in the transformed space z are broken when recovered to original space x. The position Sx and momentum S p information entropies for six low-lying states are calculated. We notice that the Sx decreases with the increasing mass barrier width a and becomes negative beyond a particular width a,while the Sp first increases with a and then decreases with it. The negative Sx exists for the probability densities that are highly localized. We find that the probability density ρ（x） for n = 1, 3, 5 are greater than 1 at position x = 0. Some interesting features of the information entropy densities ρs（x） and ρs（p） are demonstrated. The Bialynicki-Birula-Mycielski（BBM）inequality is also tested for these states and found to hold.

Energy states of the Hulthen plus Coulomb-like potential with position-dependent mass function in external magnetic fields

We need to solve a suitable exponential form of the position-dependent mass （PDM） Schr6dinger equation with a charged particle placed in the Hulthen plus Coulomb-like potential field and under the actions of the external magnetic and Aharonov-Bohm （AB） flux fields. The bound state energies and their corresponding wave functions are calculated for the spatially-dependent mass distribution function of interest in physics. A few plots of some numerical results with respect to the energy are shown.

Dynamic modeling and simulation for the rigid flexible coupling system with a non-tip mass

The rigid flexible coupling system with a mass at non-tip position of the flexible beam is studied in this paper. Using the theory about mechanics problems in a non-inertial coordinate sys- tem, the dynamic equations of the rigid flexible coupling system with dynamic stiffening are estab- lished. It is clearly elucidated for the first time that, dynamic stiffening is produced by the coupling effect of the centrifugal inertial load distributed on the beam and the transverse vibration deformation of the beam. The modeling approach in this paper successfully solves problems of popular modeling methods nowadays： the derivation process is too complex by using only one dynamic principle; a clearly theoretical mechanism for dynamic stiffening can＇ t be offered. First, the mass at non-tip po- sition is incorporated into the continuous dynamic equations of the system by use of the Dirac lunch tion and the Heaviside function. Then, based on the conclusions of orthogonalization about the nor- mal constrained modes, the finite dimensional state space equations suitable for controller design are obtained. The numerical simulation results show that： dynamic stiffening is included in the first-or- der model established in this paper, which indicates the dynamic responses of the rigid flexible cou- pling system with large overall motion accurately. The results also show that the mass has a soften- ing effect on the dynamic behavior of the flexible beam, and the effect would be more obvious when the mass has a larger mass, or lies closer to the tip of the beam.

EXISTENCE OF POSITIVE SOLUTIONS TO SEMILINEAR ELLIPTIC SYSTEMS IN R^N WITH ZERO MASS

In this paper, we prove the existence of at least one positive solution pairto the following semilinear elliptic systemby using a linking theorem, where K（x）is a positive function in L^s（R^N） for some s 〉 1and the nonnegative functions f, g ∈ C（R, R） are of quasicritical growth, superlinear atinfinity. We do not assume that f or g satisfies the Ambrosetti-Rabinowitz condition as usual. Our main result can be viewed as a partial extension of a recent result of Alves, Souto and Montenegro in [1] concerning the existence of a positive solution to the following semilinear elliptic problemand a recent result of Li and Wang in [22] concerning the existence of nontrivial solutions to a semilinear elliptic system of Hamiltonian type in R^N.