Forced Harmonic Vibration of Viscoelastic Oscillator

Cauchy Problem for Forced Harmonic Oscillator

We construct an explicit solution of the Cauchy initial value problem for the onedimensional Schrödinger equation with time-dependent Hamiltonian operator for the forced harmonic oscillator. The corresponding Green function (propagator) is derived with the help of the generalized Fourier transform and a relation with representations of the Heisenberg–Weyl group N (3) in a certain special case a...

Forced harmonic vibration of a Duffing oscillator with linear viscous damping

TheDuffing oscillator has become a classical paradigm for illustrating the remarkable jump phenomenon and other nonlinear behaviour [1,2]. The understanding gained on the basis of this low-order nonlinear systemhas helped in the development of reducedorder models of complex mechanical systems ranging from microscales to macroscales [3,4]. The nondimensional Duffing equation with damping and ext...

The Forced Harmonic Oscillator, Decoherence, and Schrödinger Cat States

The harmonic oscillator is a very significant problem in quantum mechanics, because it is one of the very few, relatively non-trivial problems that has an exact analytic solution. In addition to this, the harmonic oscillator solution and algebraic formalism has applications throughout modern physics (e.g. many particle systems, QED, quantum field theory, approximations of real systems such as m...

The Cauchy Problem for a Forced Harmonic Oscillator

We construct an explicit solution of the Cauchy initial value problem for the onedimensional Schrödinger equation with a time-dependent Hamiltonian operator for the forced harmonic oscillator. The corresponding Green function (propagator) is derived with the help of the generalized Fourier transform and a relation with representations of the Heisenberg–Weyl group N (3) in a certain special case...

Harmonic Oscillator