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Harmonic Oscillator (harmonic + oscillator)

Distribution by Scientific Domains

Physics and Astronomy	38%
Engineering	23%

Selected Abstracts

Harmonic oscillators realized using current amplifiers and grounded capacitors

INTERNATIONAL JOURNAL OF CIRCUIT THEORY AND APPLICATIONS, Issue 2 2007
George Souliotis
Abstract New configurations of harmonic oscillators, realized using current amplifier blocks and only grounded capacitors, are introduced in this article. The proposed configurations are based on a grounded inductor simulator scheme and on a loop constructed from first-order sections, respectively. Comparison with the already published topologies shows that the new configurations have attractive characteristics concerning their implementation in integrated form. Copyright © 2006 John Wiley & Sons, Ltd. [source]

Introductory quantum physics courses using a LabVIEW multimedia module

COMPUTER APPLICATIONS IN ENGINEERING EDUCATION, Issue 2 2007
Ismael Orquín
Abstract We present the development of a LabVIEW multimedia module for introductory Quantum Physics courses and our experience in the use of this application as an educational tool in learning methodologies. The program solves the time-dependent Schrödinger equation (TDSE) for arbitrary potentials. We describe the numerical method used for solving this equation, as well as some mathematical tools employed to reduce the calculation time and to obtain more accurate results. As an illustration, we present the evolution of a wave packet for three different potentials: the repulsive barrier potential, the repulsive step potential, and the harmonic oscillator. This application has been successfully integrated in the learning strategies of the course Quantum Physics for Engineering at the Polytechnic University of Valencia, Spain. © 2007 Wiley Periodicals, Inc. Comput Appl Eng Educ. 15: 124,133, 2007; Published online in Wiley InterScience (www.interscience.wiley.com); DOI 10.1002/cae.20100 [source]

Dependence of s -waves on continuous dimension: The quantum oscillator and free systems

FORTSCHRITTE DER PHYSIK/PROGRESS OF PHYSICS, Issue 12 2006
K.B. Wolf
Abstract Wavefunctions with rotational symmetry (i.e., zero angular momentum) in D dimensions, are called s -waves. In quantum quadratic systems (free particle, harmonic and repulsive oscillators), their radial parts obey Schrödinger equations with a fictitious centrifugal (for integer D , 4) or centripetal (for D = 2) potential. These Hamiltonians close into the three-dimensional Lorentz algebra so(2,1), whose exceptional interval corresponds to the critical range of continuous dimensions 0 < D < 4, where they exhibit a one-parameter family of self-adjoint extensions in ,2(,+). We study the characterization of these extensions in the harmonic oscillator through their spectra which , except for the Friedrichs extension , are not equally spaced, and we build their time evolution Green function. The oscillator is then contracted to the free particle in continuous- D dimensions, where the extension structure is mantained in the limit of continuous spectra. Finally, we compute the free time evolution of the expectation values of the Hamiltonian, dilatation generator, and square radius between three distinct sets of ,heat'-diffused localized eigenstates. This provides a simple group-theoretic description of the purported contraction/expansion of Gaussian-ring s -waves in D > 0 dimensions. [source]

Degeneracy in one-dimensional quantum mechanics: A case study

INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 7 2010
Adelio R. Matamala
Abstract In this work we study the isotonic oscillator, V(x) = Ax2 + Bx,2, on the whole line ,, < x < + , as an example of a one-dimensional quantum system with energy level degeneracy. A symmetric double-well potential with a finite barrier is introduced to study the behavior of energy pattern between both limit: the harmonic oscillator (i.e., a system without degeneracy) and the isotonic oscillator (i.e., a system with degeneracy). © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010 [source]

Degeneracy of confined D -dimensional harmonic oscillator

INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 4 2007
H. E. Montgomery Jr.
Abstract Using the mathematical properties of the confluent hypergeometric functions, the conditions for the incidental, simultaneous, and interdimensional degeneracy of the confined D -dimensional (D > 1) harmonic oscillator energy levels are derived, assuming that the isotropic confinement is defined by an infinite potential well and a finite radius Rc. Very accurate energy eigenvalues are obtained numerically by finding the roots of the confluent hypergeometric functions that confirm the degeneracy conditions. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007 [source]

Common generating function for two-dimensional hydrogen atom complete wave functions

INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 1 2007
L. Chaos-Cador
Abstract The Schrödinger equation for the two-dimensional hydrogen atom is known to be separable and integrable in circular, parabolic, and elliptical coordinates. This makes it possible to construct a common generating function for the complete wave functions of the atom in the respective coordinates. The connections with the corresponding generating function and wave functions for the harmonic oscillator are recognized and applied in this work. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007 [source]

Computation of the eigenvalues of the one-dimensional Schrödinger equation by symplectic methods

INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 4 2006
Z. Kalogiratou
Abstract The computation of high-state eigenvalues of the one-dimensional time-independent Schrödinger equation is considered by symplectic integrators. The Schrödinger equation is first transformed into a Hamiltonian canonical equation. Yoshida-type symplectic integrators are used as well as symplectic integrators based on the Magnus expansion. Numerical results are obtained for a wide range of eigenstates of the one-dimensional harmonic oscillator, the doubly anharmonic oscillator, and the Morse potential. The eigenvalues found by the symplectic methods are compared with the eigenvalues produced by Numerov-type methods. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006 [source]

Logarithmic perturbation theory for a spiked oscillator and sum rules

INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 1 2005
S. K. Bandyopadhyay
Abstract We show that logarithmic perturbation theory nicely yields the wavefunction correction terms in closed forms for the spiked perturbation ,/x2 on the first excited state of the harmonic oscillator, where the conventional Rayleigh-Schrödinger scheme is known to encounter serious problems. The study also provides a direct route to obtain several sum rules, some of which appear to be new. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005 [source]

Supershells in deformed harmonic oscillators and atomic clusters

INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 4 2002
Dennis Bonatsos
Abstract From the mathematical point of view, the appearance of supershells is a general feature of potentials having relatively sharp edges. In physics, supershells have been observed in systems of metal clusters, which are also known to exhibit an underlying shell structure with magic numbers intermediate between the magic numbers of the 3-D isotropic harmonic oscillator and those of the 3-D square well. In the present study, Nilsson's modified harmonic oscillator (without any spin,orbit interaction), as well as the 3-D q -deformed harmonic oscillator with uq(3) , soq(3) symmetry, are considered. The former model has been used for an early schematic description of shell structure in metal clusters, while the latter has been found to successfully reproduce the magic numbers of metal clusters up to 1500 atoms, the expected limit of validity for theories based on the filling of electronic shells. The systematics of the appearance of supershells in the two models will be considered, putting emphasis on the differences between the spectra of the two oscillators. While the validity of Nilsson's modified harmonic oscillator framework is limited to relatively low particle numbers, the 3-D q -deformed harmonic oscillator gives reliable descriptions of the first supershell in metal clusters, which lies within its region of validity. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002 [source]

Control of near-grazing dynamics and discontinuity-induced bifurcations in piecewise-smooth dynamical systems

INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 16 2010
Sambit Misra
Abstract This paper develops a rigorous control paradigm for regulating the near-grazing bifurcation behavior of limit cycles in piecewise-smooth dynamical systems. In particular, it is shown that a discrete-in-time linear feedback correction to a parameter governing a state-space discontinuity surface can suppress discontinuity-induced fold bifurcations of limit cycles that achieve near-tangential intersections with the discontinuity surface. The methodology ensures a persistent branch of limit cycles over an interval of parameter values near the critical condition of tangential contact that is an order of magnitude larger than that in the absence of control. The theoretical treatment is illustrated with a harmonically excited damped harmonic oscillator with a piecewise-linear spring stiffness as well as with a piecewise-nonlinear model of a capacitively excited mechanical oscillator. Copyright © 2009 John Wiley & Sons, Ltd. [source]

Band structure of a harmonically confined electron with an impenetrable boundary

PHYSICA STATUS SOLIDI (B) BASIC SOLID STATE PHYSICS, Issue 2 2004
W. Hai
Abstract We study finite-size effects of the spatially bounded quantum systems exemplified by a single-electron quantum dot with a harmonic potential and an impenetrable boundary. A general solution of the corresponding Schrödinger equation is obtained and the unique special solution for any energy is derived from the normalization and boundary conditions. The classical-mechanically allowable eigenenergies form the continuous spectrum or piecewise continuous bands with the minimum value being much less than the zero point energy of a free harmonic oscillator. As the increase of the confining size, the band widths reduce and the energies finally close to the discrete level of the free oscillator. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]

A new look at the quantum mechanics of the harmonic oscillator

ANNALEN DER PHYSIK, Issue 7-8 2007
H.A. Kastrup
Abstract In classical mechanics the harmonic oscillator (HO) provides the generic example for the use of angle and action variables and I > 0 which played a prominent role in the "old" Bohr-Sommerfeld quantum theory. However, already classically there is a problem which has essential implications for the quantum mechanics of the (,,I)-model for the HO: the transformation is only locally symplectic and singular for (q,p) = (0,0). Globally the phase space {(q,p)} has the topological structure of the plane ,2, whereas the phase space {(,,I)} corresponds globally to the punctured plane ,2 -(0,0) or to a simple cone with the tip deleted. From the properties of the symplectic transformations on that phase space one can derive the functions h0 = I, h1 = Icos , and h2 = - Isin , as the basic coordinates on {(,,I)}, where their Poisson brackets obey the Lie algebra of the symplectic group of the plane. This implies a qualitative difference as to the quantum theory of the phase space {(,,I)} compared to the usual one for {(q,p)}: In the quantum mechanics for the (,,I)-model of the HO the three hj correspond to the self-adjoint generators Kj, j = 0,1,2, of certain irreducible unitary representations of the symplectic group or one of its infinitely many covering groups, the representations being parametrized by a (Bargmann) index k > 0. This index k determines the ground state energy of the (,,I)-Hamiltonian . For an m -fold covering the lowest possible value for k is k = 1/m, which can be made arbitrarily small by choosing m accordingly! This is not in contradiction to the usual approach in terms of the operators Q and P which are now expressed as functions of the Kj, but keep their usual properties. The richer structure of the Kj quantum model of the HO is "erased" when passing to the simpler (Q,P)-model! This more refined approach to the quantum theory of the HO implies many experimental tests: Mulliken-type experiments for isotopic diatomic molecules, experiments with harmonic traps for atoms, ions and BE-condensates, with charged HOs in external electric fields and the (Landau) levels of charged particles in external magnetic fields, with the propagation of light in vacuum, passing through strong external electric or magnetic fields. Finally it may lead to a new theoretical estimate for the quantum vacuum energy of fields and its relation to the cosmological constant. [source]

Equilibration of a dissipative quantum oscillator

ANNALEN DER PHYSIK, Issue 5-6 2007
V. Ambegaokar
Abstract An explicit demonstration is given of a harmonic oscillator in equilibrium approaching the equilibrium of a corresponding interacting system by coupling it to a thermal bath consisting of a continuum of harmonic oscillators. [source]

Harmonic oscillators realized using current amplifiers and grounded capacitors

Current differential amplifiers: new circuits and applications

INTERNATIONAL JOURNAL OF CIRCUIT THEORY AND APPLICATIONS, Issue 6 2001
George Souliotis
Abstract New CMOS current differential amplifiers are proposed suitable for analogue signal processing at high frequencies. They consist of simple current mirrors, which are easy to design and to implement in IC form. Low-voltage low-power design is feasible. Relying on these devices a number of applications are obtained, including lossy and lossless integrators, simulated inductors, active filters, and harmonic oscillators. Theoretical expressions are given for all of the proposed new circuits. The verification of the circuits is also achieved by simulation. Copyright 2001 © John Wiley & Sons, Ltd. [source]

Supershells in deformed harmonic oscillators and atomic clusters

Indefinite oscillators and black-hole evaporation

ANNALEN DER PHYSIK, Issue 10-11 2009
C. Kiefer
Abstract We discuss the dynamics of two harmonic oscillators of which one has a negative kinetic term. This model mimics the Hamiltonian in quantum geometrodynamics, which possesses an indefinite kinetic term. We solve for the time evolution in both the uncoupled and coupled case. We use this setting as a toy model for studying some possible aspects of the final stage of black-hole evaporation. We assume that one oscillator mimics the black hole, while the other mimics Hawking radiation. In the uncoupled case, the negative term leads to a squeezing of the quantum state, while in the coupled case, which includes back reaction, we get a strong entangled state between the mimicked black hole and the radiation. We discuss the meaning of this state. We end by analyzing the limits of this model and its relation to more fundamental approaches. [source]