Paraquantum generalized harmonic oscillator in the Lewis-Riesenfeld invariants operator method

2012 ◽  
Author(s):  
M. Harrat ◽  
N. Mebarki ◽  
A. Redouane Salah
Keyword(s):  
Harmonic Oscillator ◽  
Operator Method ◽  
Generalized Harmonic Oscillator

UNITARY TRANSFORMATION APPROACH FOR THE PHASE OF THE DAMPED DRIVEN HARMONIC OSCILLATOR

2003 ◽  
Vol 17 (26) ◽  
pp. 1365-1376 ◽  
Author(s):  
JEONG-RYEOL CHOI
Keyword(s):  
Wave Function ◽  
Harmonic Oscillator ◽  
Unitary Transformation ◽  
Operator Method ◽  
Classical Equation ◽  
Transformation Method ◽  
Invariant Operator ◽  
Harmonic Oscillators ◽  
Parabolic Cylinder ◽  
Parabolic Cylinder Function

Using the invariant operator method and the unitary transformation method together, we obtained discrete and continuous solutions of the quantum damped driven harmonic oscillator. The wave function of the underdamped harmonic oscillator is expressed in terms of the Hermite polynomial while that of the overdamped harmonic oscillator is expressed in terms of the parabolic cylinder function. The eigenvalues of the underdamped harmonic oscillator are discrete while that of the critically damped and the overdamped harmonic oscillators are continuous. We derived the exact phases of the wave function for the underdamped, critically damped and overdamped driven harmonic oscillator. They are described in terms of the particular solutions of the classical equation of motion.

scholarly journals Analisis Energi Osilator Harmonik Menggunakan Metode Path Integral Hypergeometry dan Operator

2016 ◽  
Vol 2 (02) ◽  
pp. 7
Author(s):  
Fuzi Marati Sholihah ◽  
Suparmi S ◽  
Viska Inda Variani
Keyword(s):  
Energy Spectrum ◽  
Harmonic Oscillator ◽  
Path Integral ◽  
Integral Method ◽  
Schrodinger Equation ◽  
Energy Levels ◽  
Operator Method ◽  
One Dimensional ◽  
Equation Analysis ◽  
Path Integral Method

<span>Solution of the harmonic oscillator equation has a goal to get the energy levels of particles <span>moving harmonic. The energy spectrums of one dimensional harmonic oscillator are <span>analyzed by 3 methods: path integral, hypergeometry and operator. Analysis of the energy <span>spectrum by path integral method is examined with Schrodinger equation. Analysis of the <span>energy spectrum by operator method is examined by Hamiltonian in operator. Analysis of <span>harmonic oscillator energy by 3 methods: path integral, hypergeometry and operator are <span>getting same results 𝐸 = ℏ𝜔 (𝑛 + <span>1 2<span>)</span></span></span></span></span></span><br /></span></span></span>

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