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An Asymmetric Harmonic Oscillator
The solution of one-dimensional asymmetric quantum harmonic oscillator is presented. The asymmetry can be realized, for example, by using two...
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Harmonic Oscillator
Lights, sounds, vibrations—such waves we see daily are mostly understood as harmonic oscillations supported in various media. These harmonic...
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Very Weak Solution of the Discrete Wave Equation for Harmonic Oscillator
In this paper, we announce some preliminary findings of the joint work with [6] for the wave equation with Schrödinger operator. In particular, we...
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Sharp Strichartz type estimates for the Schrödinger equation associated with harmonic oscillator
In this article we study the Schrödinger equation associated with Harmonic oscillator in the form of Strichartz type inequality. We give simple...
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A Note on the Heat Kernel for the Rescaled Harmonic Oscillator from Two Step Nilpotent Lie Groups
In this note, we use Schrödinger representations and the Fourier transform on two step nilpotent Lie groups to compute the explicit formula of the...
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Motion of Driven Damped Oscillator in Phase Space
By numerically solving differential equation of motion using 4th order Runge–Kutta method, in this chapter, we have numerically plotted trajectories...
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Minimal Unit Vector Fields on Oscillator Groups
In this paper we treat minimal left-invariant unit vector fields on oscillator group and their relations with the ones that defines a harmonic map....
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Truly Nonlinear Oscillator with Limit Cycles and Harmonic Solutions
This paper presents some classes of truly nonlinear oscillatory equations of polynomial type. It has been shown that these classes can generate many...
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Variational Monte Carlo Method Applied to Ground State of Simple Harmonic Oscillator Using Acceptance-Rejection Sampling Utilizing Mathematica
This chapter provides practical demonstration of obtaining ground state energy and eigenfunction of simple harmonic oscillator using variational...
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Global existence for the semi-linear wave/Klein–Gordon equation associated to the harmonic oscillator in low dimensions
We show that the small solution for the semi-linear wave/Klein–Gordon equation associated to the harmonic oscillator exists globally in dimension 1...
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Quantum simulation of discretized harmonic oscillator
In this work, we conduct a quantum simulation of a particle in a harmonic oscillator potential on a quantum chip provided by IBM quantum experience...
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Interface asymptotics of Wigner—Weyl distributions for the Harmonic Oscillator
We prove several types of scaling results for Wigner distributions of spectral projections of the isotropic Harmonic oscillator on ℝ d . In prior work,...
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A novel adaptive harmonic balance method with an asymptotic harmonic selection
The harmonic balance method (HBM) is one of the most widely used methods in solving nonlinear vibration problems, and its accuracy and computational...
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Quantum forced oscillator via Wigner transform
In this paper we review the basic results concerning the Wigner transform and critically discuss the problem of the reversibility. Then we completely...
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Reducibility of the Linear Quantum Harmonic Oscillators Under Quasi-periodic Reversible Perturbation
In this paper, we establish the reducibility of a class of linear coupled quantum harmonic oscillator systems under time quasi-periodic,...
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Harmonic Balance with Small Signal Perturbation
Investigating perturbations of a periodic steady state of an electric circuit is of interest e.g. for small signal responses, noise analysis or the...
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Scattering States of the Inverted Oscillator and Its Supersymmetric Partners
The inverted oscillator (repulsive oscillator or parabolic potential barrier) is an exactly solvable potential with scattering states and infinite...
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Van der Pol Oscillator under Random Noise
AbstractThe first approximations are found to the expectation and the dispersion function of the solution for a mathematical model of an oscillator...
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Reconstruction of the Fourier expansion of a periodic force acting on an oscillator
The problem of determining a periodic external force acting on a non-linear self-oscillating system of general type (the Liénard oscillator) is...