Open AccessHamiltonian matrix representation of harmonic oscillator system with Linear-Cubic-Quartic (LCQ) perturbation
Author(s) -
Nila Prasetya Aryani,
Herry F. Lalus,
Siti Wahyuni,
F D Ratnasari,
I Akhlis
Publication year - 2021
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1918/2/022024
Subject(s) - harmonic oscillator , hamiltonian (control theory) , mathematics , perturbation (astronomy) , creation and annihilation operators , mathematical analysis , quantum mechanics , physics , mathematical optimization , quantum
In this paper, we analyze the matrix representation of the energy operator (Hamiltonian) of the harmonic oscillator system when this system is perturbed by an LCQ perturbation. The LCQ perturbation is simultaneously acted on this system, so the total Hamiltonian is a summation of the pure oscillator harmonic operator term (in the annihilation and creation operator statement) and the three perturbation terms. In this work, we use three different small parameters for each term of the perturbation for keeping the generality. We use the simple algebraic method by using the Dirac notation and the well-known base vector of harmonic oscillator to analyze this problem. Next, we present every term of this operator in matrix representation and then adding them for finding matrix representation for the total Hamiltonian.