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The harmonic oscillator propagator
American Journal of Physics, 1998 The published version is located at http://ajp.aapt.org/resource/1/ajpias/v66/i7/p583_s1The Feynman propagator for the harmonic oscillator is evaluated by a variety of path-integral-based means.583 ...
Holstein, BR
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Nonlinear harmonic oscillators
Journal of Physics A: Mathematical and General, 2002This paper deals with the existence of assembles of an arbitrary number of complex oscillators, or equivalently of an arbitrary even number of real oscillators, characterized by Newtonian equations of motion (``acceleration equal force'') with one-body velocity-dependent linear forces and many-body velocity-independent cubic forms, all the nonsingular ...
CALOGERO, Francesco, INOZEMTSEV V. I.
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Harmonic Oscillators with Nonlinear Damping
International Journal of Bifurcation and Chaos, 2017Dynamical systems with special properties are continually being proposed and studied. Many of these systems are variants of the simple harmonic oscillator with nonlinear damping. This paper characterizes these systems as a hierarchy of increasingly complicated equations with correspondingly interesting behavior, including coexisting attractors, chaos ...
Julien Clinton Sprott +1 more
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Nonadiabatic Harmonic Oscillator
The Physics of Fluids, 1970Nonadiabatic changes in the action integral are estimated for the special case of even ω(t) by using a steepest-descent method to evaluate an integral of Vandervoort. The results are found to be in good agreement with a numerical example.
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SIAM Journal on Applied Mathematics, 1973
The normal modes of oscillation of a circular array of linked harmonic oscillators are considered from a variety of points of view, and a representation of the oscillations of an infinite array in terms of contour integrals is given.
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The normal modes of oscillation of a circular array of linked harmonic oscillators are considered from a variety of points of view, and a representation of the oscillations of an infinite array in terms of contour integrals is given.
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1993
This chapter is the closest in these notes to what is usually called “Quantum Mechanics”. The present version is considerably shorter than the original French. It thus becomes more obvious that its main topic is not really elementary quantum mechanics, but rather elementary Fock space, and the quantum analogue of finite dimensional Gaussian random ...
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This chapter is the closest in these notes to what is usually called “Quantum Mechanics”. The present version is considerably shorter than the original French. It thus becomes more obvious that its main topic is not really elementary quantum mechanics, but rather elementary Fock space, and the quantum analogue of finite dimensional Gaussian random ...
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On then-dimensional harmonic oscillator
Annali di Matematica Pura ed Applicata, 1979In this paper, various oscillatory properties of solutions of the scalar equation x″+q(t)x=0 are extended to the vector equation u″+Q(t)u=0.
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2014
We start this part devoted to lumped parameter models by studying a simple paradigmatic model in physics: the harmonic oscillator. In principle, it corresponds to a mechanical system consisting of a mass connected to a spring and a dashpot (see Fig.
Alfredo Bermúdez +2 more
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We start this part devoted to lumped parameter models by studying a simple paradigmatic model in physics: the harmonic oscillator. In principle, it corresponds to a mechanical system consisting of a mass connected to a spring and a dashpot (see Fig.
Alfredo Bermúdez +2 more
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1996
The harmonic oscillator provides a unique opportunity to study with simple mathematics the properties acquired by a mechanical system in permanent contact with the zeropoint field, and to assess with a specific example the merit of the assumption that the classical particle becomes through this interaction a quantum object.
Luis de la Peña, Ana María Cetto
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The harmonic oscillator provides a unique opportunity to study with simple mathematics the properties acquired by a mechanical system in permanent contact with the zeropoint field, and to assess with a specific example the merit of the assumption that the classical particle becomes through this interaction a quantum object.
Luis de la Peña, Ana María Cetto
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2018
Abstract This chapter discusses the harmonic oscillator, which is a model ubiquitous to all branches of physics. The harmonic oscillator is a system with well-known solutions and has been fully investigated since it was first developed by Robert Hooke in the seventeenth century.
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Abstract This chapter discusses the harmonic oscillator, which is a model ubiquitous to all branches of physics. The harmonic oscillator is a system with well-known solutions and has been fully investigated since it was first developed by Robert Hooke in the seventeenth century.
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