Instanton solutions on the polymer harmonic oscillator

Periodic Solutions of the Duffing Harmonic Oscillator by He's Energy Balance Method

Duffing harmonic oscillator is a common model for nonlinear phenomena in science and engineering. This paper presents He´s Energy Balance Method (EBM) for solving nonlinear differential equations. Two strong nonlinear cases have been studied analytically. Analytical results of the EBM are compared with the solutions obtained by using He´s Frequency Amplitude Formulation (FAF) and numerical solu...

Harmonic Oscillator

periodic solutions of the duffing harmonic oscillator by he's energy balance method

duffing harmonic oscillator is a common model for nonlinear phenomena in science and engineering. this paper presents he´s energy balance method (ebm) for solving nonlinear differential equations. two strong nonlinear cases have been studied analytically. analytical results of the ebm are compared with the solutions obtained by using he´s frequency amplitude formulation (faf) and numerical solu...

Finite-dimensional solutions of coupled harmonic oscillator quantum systems

This paper describes a quantum system consisting of a onedimensional chain of M identical harmonic oscillators coupled by means of springs. We approach this as a Wigner Quantum System, not imposing the canonical commutation relations, but using instead weaker relations following from the compatibility of Hamilton’s equations and the Heisenberg equations. We show that a class of solutions can be...

Optional Problems on the Harmonic Oscillator

â φα = αφα , with α a complex number (see next page for a discussion of â and â†). Such a state is called a “coherent state”. Coherent states turn out to be the closest quantum analog of classical states with well-defined amplitudes and phases, and are extremely important in e.g. the quantum mechanical description of laser light, radio cavities, Bose-Einstein condensates, and just about everyth...