Bound States Research Papers - Academia.edu (original) (raw)

In this study, the analytical solutions of the Dirac equation have been presented for the Hulthén and Eckart potentials by applying an approximation to centrifugal-like term in the case of spin symmetry, Delta(r) = C = constant, and... more

In this study, the analytical solutions of the Dirac equation have been presented for the Hulthén and Eckart potentials by applying an approximation to centrifugal-like term in the case of spin symmetry, Delta(r) = C = constant, and pseudospin symmetry, Sigma(r) = C = constant, for any spin-orbit quantum number kappa. The energy eigenvalues and corresponding spinor wave functions are

The determination of extractable trace metals in sediments using sequential extraction procedures has been performed in many laboratories within the last ten years in order to study environmental pathways (e.g. mobility of metals,... more

The determination of extractable trace metals in sediments using sequential extraction procedures has been performed in many laboratories within the last ten years in order to study environmental pathways (e.g. mobility of metals, bounding states). However, the results obtained by different laboratories could hardly be compared due to lack of harmonized schemes. Owing to the need for standardization and subsequent validation of extraction schemes for sediment analysis, the Measurements and Testing Programme (formerly BCR Programme) of the European Commission has organized a project to adopt a sequential extraction procedure that could be used as a mean of comparison of data of extractable trace metals in sediments. A scheme was designed after a series of investigations on existing schemes and tested in interlaboratory studies. This paper presents the results of two round-robin exercises on extractable trace metals using this sequential extraction protocol and describes the final version of the extraction procedure amended according to the most recent improvements.

A universal controller is designed for cascade systems, involving dynamic uncertainty, unknown nonlinearities, exogenous disturbances and/or time-varying parameters, capable of guaranteeing prescribed performance for the output tracking... more

A universal controller is designed for cascade systems, involving dynamic uncertainty, unknown nonlinearities, exogenous disturbances and/or time-varying parameters, capable of guaranteeing prescribed performance for the output tracking error, as well as uniformly bounded signals in the closed loop. By prescribed performance we mean that the output tracking error should converge to a predefined arbitrarily small residual set, with convergence rate no less than a certain prespecified value, exhibiting maximum overshoot less than a sufficiently small preassigned constant. The proposed control scheme is of low complexity, utilizes partial state feedback and requires reduced levels of a priori system knowledge. The results can be easily extended to systems affected by bounded state measurement errors, as well as to MIMO nonlinear systems in block triangular form. Simulations clarify and verify the approach.

Non-minimum phase tracking control is studied for boost and buck-boost power converters. A sliding mode control algorithm is developed to track directly a causal voltage tracking profile given by an exogenous system. The approximate... more

Non-minimum phase tracking control is studied for boost and buck-boost power converters. A sliding mode control algorithm is developed to track directly a causal voltage tracking profile given by an exogenous system. The approximate causal output non-minimum phase asymptotic tracking in non-linear boost and buck-boost power converters is addressed via sliding mode control using a dynamic sliding manifold (DSM). Use of DSM allows the stabilization of the internal dynamics when the output tracking error tends asymptotically to zero in the sliding mode. The sliding mode controller with DSM links features of conventional sliding mode control (insensitivity to matched non-linearities and disturbances) and a conventional dynamic compensator (accommodation to unmatched disturbances). Numerical examples demonstrate the effectiveness of the sliding mode controller even for a known time-varying load. Copyright © 2003 John Wiley & Sons, Ltd.

An exact quantization rule for the Schr\"{o}dinger equation is presented. In the exact quantization rule, in addition to NpiN\piNpi, there is an integral term, called the quantum correction. For the exactly solvable systems we find that the... more

An exact quantization rule for the Schr\"{o}dinger equation is presented. In the exact quantization rule, in addition to NpiN\piNpi, there is an integral term, called the quantum correction. For the exactly solvable systems we find that the quantum correction is an invariant, independent of the number of nodes in the wave function. In those systems, the energy levels of all the bound states can be easily calculated from the exact quantization rule and the solution for the ground state, which can be obtained by solving the Riccati equation. With this new method, we re-calculate the energy levels for the one-dimensional systems with a finite square well, with the Morse potential, with the symmetric and asymmetric Rosen-Morse potentials, and with the first and the second P\"{o}schl-Teller potentials, for the harmonic oscillators both in one dimension and in three dimensions, and for the hydrogen atom.

In our research group, we develop novel dots-in-a-well (DWELL) photodetectors that are a hybrid of the quantum dot infrared photodetector (QDIP). The DWELL detector consists of an active region composed of InAs quantum dots embedded in... more

In our research group, we develop novel dots-in-a-well (DWELL) photodetectors that are a hybrid of the quantum dot infrared photodetector (QDIP). The DWELL detector consists of an active region composed of InAs quantum dots embedded in InGaAs quantum wells. By adjusting the InGaAs well thickness, our structure allows for the manipulation of the operating wavelength and the nature of the

Given an operator L acting on a function space, the J-matrix method consists of finding a sequence y_n of functions such that the operator L acts tridiagonally on y_n with respect to n. Once such a tridiagonalization is obtained, a number... more

Given an operator L acting on a function space, the J-matrix method consists of finding a sequence y_n of functions such that the operator L acts tridiagonally on y_n with respect to n. Once such a tridiagonalization is obtained, a number of characteristics of such an operator L can be obtained. In particular, information on eigenvalues and eigenfunctions, bound states, spectral decompositions, etc. can be obtained in this way. We review the general set-up, and we discuss two examples in detail; the Schrodinger operator with Morse potential and the Lame equation.

It is well known that the harmonic oscillator potential can be solved by using raising and lowering operators. This operator method can be generalized with the help of supersymmetry and the concept of ``shape-invariant''... more

It is well known that the harmonic oscillator potential can be solved by using raising and lowering operators. This operator method can be generalized with the help of supersymmetry and the concept of ``shape-invariant'' potentials. This generalization allows one to calculate the energy eigenvalues and eigenfunctions of essentially all known exactly solvable potentials in a simple and elegant manner.

The principle of nuclear democracy is invoked to prove the formation of stable quantized gravitational bound states of primordial black holes called Holeums. The latter come in four varieties: ordinary Holeums H, Black Holeums BH, Hyper... more

The principle of nuclear democracy is invoked to prove the formation of stable quantized gravitational bound states of primordial black holes called Holeums. The latter come in four varieties: ordinary Holeums H, Black Holeums BH, Hyper Holeums HH and the massless Lux Holeums LH.These Holeums are invisible because the gravitational radiation emitted by their quantum transitions is undetectable now. The

Recent studies of QCD Green's functions and their applications in hadronic physics are reviewed. We discuss the definition of the generating functional in gauge theories, in particular, the rôle of redundant degrees of freedom,... more

Recent studies of QCD Green's functions and their applications in hadronic physics are reviewed. We discuss the definition of the generating functional in gauge theories, in particular, the rôle of redundant degrees of freedom, possibilities of a complete gauge fixing versus gauge fixing in presence of Gribov copies, BRS invariance and positivity. The apparent contradiction between positivity and colour antiscreening in combination with BRS invariance in QCD is considered. Evidence for the violation of positivity by quarks and transverse gluons in the covariant gauge is collected, and it is argued that this is one manifestation of confinement. We summarise the derivation of the Dyson-Schwinger equations (DSEs) of QED and QCD. For the latter, the implications of BRS invariance on the Green's functions are explored. The possible influence of instantons on DSEs is discussed in a two-dimensional model. In QED in (2+1) and (3+1) dimensions, the solutions for Green's functions provide tests of truncation schemes which can under certain circumstances be extended to the DSEs of QCD. We discuss some limitations of such extensions and assess the validity of assumptions for QCD as motivated from studies in QED. Truncation schemes for DSEs are discussed in axial and related gauges, as well as in the Landau gauge. Furthermore, we review the available results from a systematic non-perturbative expansion scheme established for Landau gauge QCD. Comparisons to related lattice results, where available, are presented. The applications of QCD Green's functions to hadron physics are summarised. Properties of ground state mesons are discussed on the basis of the ladder Bethe-Salpeter equation for quarks and antiquarks. The Goldstone nature of pseudoscalar mesons and a mechanism for diquark confinement beyond the ladder approximation are reviewed. We discuss some properties of ground state baryons based on their description as Bethe-Salpeter/Faddeev bound states of quark-diquark correlations in the quantum field theory of confined quarks and gluons.

We study, in detail, the supersymmetric quantum mechanics of charge-(1,1) monopoles in N=2 supersymmetric Yang-Mills-Higgs theory with gauge group SU(3) spontaneously broken to U(1) x U(1). We use the moduli space approximation of the... more

We study, in detail, the supersymmetric quantum mechanics of charge-(1,1) monopoles in N=2 supersymmetric Yang-Mills-Higgs theory with gauge group SU(3) spontaneously broken to U(1) x U(1). We use the moduli space approximation of the quantised dynamics, which can be expressed in two equivalent formalisms: either one describes quantum states by Dirac spinors on the moduli space, in which case the Hamiltonian is the square of the Dirac operator, or one works with anti-holomorphic forms on the moduli space, in which case the Hamiltonian is the Laplacian acting on forms. We review the derivation of both formalisms, explicitly exhibit their equivalence and derive general expressions for the supercharges as differential operators in both formalisms. We propose a general expression for the total angular momentum operator as a differential operator, and check its commutation relations with the supercharges. Using the known metric structure of the moduli space of charge-(1,1) monopoles we show that there are no quantum bound states of such monopoles in the moduli space approximation. We exhibit scattering states and compute corresponding differential cross sections.

We introduce a family of relativistic non-rigid non-inertial frames as a gauge fixing of the description of N positive energy particles in the framework of parametrized Minkowski theories. Then we define a multi-temporal quantization... more

We introduce a family of relativistic non-rigid non-inertial frames as a gauge fixing of the description of N positive energy particles in the framework of parametrized Minkowski theories. Then we define a multi-temporal quantization scheme in which the particles are quantized, but not the gauge variables describing the non-inertial frames: {\it they are considered as c-number generalized times}. We study the coupled Schroedinger-like equations produced by the first class constraints and we show that there is {\it a physical scalar product independent both from time and generalized times and a unitary evolution}. Since a path in the space of the generalized times defines a non-rigid non-inertial frame, we can find the associated self-adjoint effective Hamiltonian hatHni\hat{H}_{ni}hatHni for the non-inertial evolution: it differs from the inertial energy operator for the presence of inertial potentials and turns out to be {\it frame-dependent} like the energy density in general relativity. After a separation of the relativistic center of mass from the relative variables by means of a recently developed relativistic kinematics, inside hatHni\hat{H}_{ni}hatHni we can identify the self-adjoint relative energy operator (the invariant mass) hatcalM{\hat{\cal M}}hatcalM corresponding to the inertial energy and producing the same levels for the spectra of atoms as in inertial frames. Instead the (in general time-dependent) effective Hamiltonian is responsible for the interferometric effects signalling the non-inertiality of the frame but is not interpretable as an energy like in the case of time-dependent c-number external electro-magnetic fields.