A Quadratic-quartic-quintic (Qqq) Perturbation On Harmonic Oscillator: Hamiltonian Matrix Representation

This paper discusses a one-dimensional harmonic oscillator system subjected to simultaneous quadratic-quartic-quintic perturbation. The main objective of this paper is to calculate the matrix representation of its Hamiltonian. To keep more generally, these three perturbation terms use different small parameters. The method used in this paper is the standard algebraic method using Dirac notation with the bases that have also been shown. The results of the analysis that has been carried out, it is obtained in the form of the Hamiltonian matrix representation of this system which contains the three different small parameters. If the three parameters are chosen to be zero (without perturbation), the matrix form will be reduced to a standard harmonic oscillator matrix.Keywords: QQQ perturbation; harmonic oscillator, Hamiltonian matrix representation