Square root of the harmonic oscillator

A square root of the harmonic oscillator

Allowing for the inclusion of the parity operator, it is possible to construct a model of an oscillator whose Hamiltonian admits an exact square root which is rather different from the conventional approach based on creation and annihilation operators. We outline such a model, the method of solution and some generalisations. 03.65.Ge, 03.65.Fd Typeset using REVTEX In memory of Lorella M Jones w...

On the square root of quadratic matrices

Here we present a new approach to calculating the square root of a quadratic matrix. Actually, the purpose of this article is to show how the Cayley-Hamilton theorem may be used to determine an explicit formula for all the square roots of $2times 2$ matrices.

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...

Quantizing the damped harmonic oscillator

We consider the Fermi quantization of the classical damped harmonic oscillator (dho). In past work on the subject, authors double the phase space of the dho in order to close the system at each moment in time. For an infinite-dimensional phase space, this method requires one to construct a representation of the CAR algebra for each time. We show that unitary dilation of the contraction semigrou...