Reply to the ‘Comment on ‘Generalization of the Darboux transformation and generalized harmonic oscillators’’

2005 ◽  
Vol 38 (25) ◽  
pp. 5837-5839 ◽  
Author(s):  
Dae-Yup Song ◽  
John R Klauder
Keyword(s):  
Darboux Transformation ◽  
Harmonic Oscillators ◽  
Generalized Harmonic Oscillators

Generalized Harmonic Oscillators: Velocity Dependent Frequencies

2001 ◽  
Author(s):  
Ronald E. Mickens
Keyword(s):  
Nonlinear Oscillator ◽  
First Integral ◽  
Harmonic Oscillators ◽  
System Of Equations ◽  
Research Grants ◽  
Physical Systems ◽  
New Class ◽  
Generalized Harmonic Oscillators ◽  
Special Cases ◽  
Oscillator Equations

Abstract Preliminary results are given on a new class of nonlinear oscillator equations that generalize those of the usual linear harmonic case. These equations take the form ẋ = f(x)y and ẏ = −g(y)x, where f(x) and g(y) are continuous with first derivatives, and f(0) > 0, g(0) > 0. Of interest is the fact that these equations have a first-integral, i.e., there exists a function H(x,y) such that along a particular trajectory in the (x,y) phase space, H(x,y) = constant. We work out several general results related to this system of equations and illustrate them with several special cases that correspond to models of physical systems. The work reported here was supported in part by research grants from DOE and the MBRS-SCORE Program at Clark Atlanta University.

scholarly journals Exact wave functions for generalized harmonic oscillators

2011 ◽  
Vol 32 (4) ◽  
pp. 352-361 ◽  
Author(s):  
Nathan Lanfear ◽  
Raquel M. López ◽  
Sergei K. Suslov
Keyword(s):  
Wave Functions ◽  
Harmonic Oscillators ◽  
Generalized Harmonic Oscillators
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