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The Harmonic Oscillator

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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Valons and harmonic oscillators

Physical Review D, 1981
The valon distribution derived by Hwa is compared with the valence-quark distribution from the covariant-harmonic-oscillator wave function which correctly describes the proton-form-factor behavior, and which provides a covariant representation of the hadron mass spectra.
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The Harmonic Oscillator

2015
The first truly significant application of the quantization conditions of the previous chapter concerns the determination of the eigenvalues of the energy for a one-dimensional oscillator. In this section we shall limit ourselves to obtain only some qualitative conditions on the energy levels of the oscillator, mainly with the purpose of giving to the ...
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Coupled Harmonic Oscillations

1988
Coupled oscillations occur in many regions of physics. The Raman and infrared spectra, for example, have their origin in the coupled oscillations of atoms within the molecule. The analysis of these oscillations gives information not only on the structure of the molecule but also on the binding forces.
Erich W. Schmid   +2 more
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Energy harvesting in the super-harmonic frequency region of a twin-well oscillator

, 2012
Nonlinear dynamical systems exhibit super-harmonic resonances that can activate large-amplitude motions at fraction integers of the fundamental frequency of the system.
Ravindra Masana, M. Daqaq
semanticscholar   +1 more source

Harmonic Oscillator

Mathematical Methods for Oscillations and Waves, 2020

semanticscholar   +1 more source

Partition Function for the Harmonic Oscillator

1992
We start by making the following changes from Minkowski real time t = x0 to Euclidean “time” τ = tE:
Walter Dittrich, Martin Reuter
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The Harmonic Oscillator

2010
In this chapter we shall review the spectral properties of the harmonic oscillator, i.e.
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The “Maslov Anomaly” for the Harmonic Oscillator

1992
Specializing the discussion of the previous section to the harmonic oscillator we have for \(N = 1,\ \eta ^{a} = (p,x),\ a = 1,2,\ \eta ^{1} \equiv p,\ \eta ^{2} \equiv x\) $$\displaystyle{ H(p,x) = \frac{1} {2}\eta ^{a}\eta ^{a} = \frac{1} {2}{\bigl (p^{2} + x^{2}\bigr )}\;. }$$ (30.1) The only conserved quantity is J = H.
Martin Reuter, Walter Dittrich
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The Quantum Harmonic Oscillator

2018
The oscillator Hamiltonian in the coordinate representation is: $$\hat{H} = {p^{2} \over 2m} +\frac{1}{2} m \omega ^{2} x^{2}.$$
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