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Bulletin of the Korean Chemical Society (BKCS)

ISSN 0253-2964(Print)
ISSN 1229-5949(Online)
Volume 25, Number 2
BKCSDE 25(2)
February 20, 2004 

 
Title
Canonical Transformations for Time-Dependent Harmonic Oscillators
Author
Tae Jun Park
Keywords
Canonical, Transformation, Time-dependent, Harmonic, Oscillator
Abstract
A canonical transformation changes variables such as coordinates and momenta to new variables preserving either the Poisson bracket or the commutation relations depending on whether the problem is classical or quantal respectively. Classically canonical transformations are well established as a powerful tool for solving differential equations. Quantum canonical transformations have been defined and used relatively recently because of the non-commutativeness of the quantum variables. Three elementary canonical transformations and their composite transformations have quantum implementations. Quantum canonical transformations have been mostly used in time-independent Schrodinger equations and a harmonic oscillator with time-dependent angular frequency is probably the only time-dependent problem solved by these transformations. In this work, we apply quantum canonical transformations to a harmonic oscillator in which both angular frequency and equilibrium position are time-dependent.
Page
285 - 288
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