A molecular system adsorbed on a dielectric surface is modeled as a damped harmonic oscillator driven by a sinusoidal external force. The exact propagator and wavefunction through the Feynman path integral method are obtained. The second-quantization of this system is carried out. Expectation values of several physical quantities are evaluartd. The amplitude for transitions between harmonic osc...

In this work, some novel approximate analytical and numerical solutions to the forced damped driven nonlinear (FDDN) pendulum equation relation equations of motion on pivot vertically for arbitrary angles are obtained. The approximation is derived in terms Jacobi elliptic functions with modulus. For approximations, Chebyshev collocation method introduced analyzing motion. Moreover, using MATHEM...

Quantization of a damped harmonic oscillator leads to so called Bateman’s dual system. The corresponding Bateman’s Hamiltonian, being a self-adjoint operator, displays the discrete family of complex eigenvalues. We show that they correspond to the poles of energy eigenvectors and the corresponding resolvent operator when continued to the complex energy plane. Therefore, the corresponding genera...

In this work, transient resonant motions excited in linearised scattering interactions are approximated using a simple damped harmonic oscillator model. The scattering interactions considered involve the diffraction of an incident wave-train with a dominant regular timeharmonic component by structures which enclose a portion of the free surface. Provided a single resonant mode only is excited s...

Abstract. In this paper we point out the existence of a remarkable nonlocal transformation between the damped harmonic oscillator and a modified Emden type nonlinear oscillator equation with linear forcing, ẍ+αxẋ+βx+γx = 0,which preserves the form of the time independent integral, conservative Hamiltonian and the equation of motion. Generalizing this transformation we prove the existence of non...

The stochastic dynamics of the damped harmonic oscillator in a heat bath is simulated with an algorithm that is exact for time steps of arbitrary size. Exact analytical results are given for correlation functions and power spectra in the form they acquire when computed from experimental time-lapse recordings. Three applications are discussed: (i) The effects of finite sampling rate and time, de...

PURPOSE To introduce a new model describing human in vivo corneal deswelling after hypoxic contact lens wear, based on a damped harmonic oscillator, which can describe an overshoot in corneal deswelling, to compare this new model with the currently used exponential model, and also to test whether a diurnal variation in baseline corneal thickness exists that would have to be taken into considera...