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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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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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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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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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1994
In this section I will put the hamwnic oscillator in its place-on a pedestaL Not only is it a system that can be exactly solved (in classical and quantum theory) and a superb pedagogical tool (which will be repeatedly exploited in this text), but it is also a system of great physical relevance.
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In this section I will put the hamwnic oscillator in its place-on a pedestaL Not only is it a system that can be exactly solved (in classical and quantum theory) and a superb pedagogical tool (which will be repeatedly exploited in this text), but it is also a system of great physical relevance.
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1995
As an extended example of Newtonian dynamics, let us examine the motion of a particle under the influence of a force whose magnitude is proportional to the displacement of the particle from an equilibrium position, and whose direction is toward that equilibrium position.
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As an extended example of Newtonian dynamics, let us examine the motion of a particle under the influence of a force whose magnitude is proportional to the displacement of the particle from an equilibrium position, and whose direction is toward that equilibrium position.
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1991
Abstract In both classical and quantum physics the harmonic oscillator is one of the most important physical systems [1–4]. Furthermore, because of the simplicity and symmetry of the Hamiltonian operator, the quantum mechanical oscillator is particularly suited to analysis by abstract operator methods.
O L De Lange, R E Raab
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Abstract In both classical and quantum physics the harmonic oscillator is one of the most important physical systems [1–4]. Furthermore, because of the simplicity and symmetry of the Hamiltonian operator, the quantum mechanical oscillator is particularly suited to analysis by abstract operator methods.
O L De Lange, R E Raab
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