84 research outputs found
On Integrability of Nonautonomous Nonlinear Schroedinger Equations
We show, in general, how to transform the nonautonomous nonlinear
Schroedinger equation with quadratic Hamiltonians into the standard autonomous
form that is completely integrable by the familiar inverse scattering method in
nonlinear science. Derivation of the corresponding equivalent nonisospectral
Lax pair is outlined. A few simple integrable systems are discussed.Comment: 15 pages, no figure
Exact Wave Functions for Generalized Harmonic Oscillators
We transform the time-dependent Schroedinger equation for the most general
variable quadratic Hamiltonians into a standard autonomous form. As a result,
the time-evolution of exact wave functions of generalized harmonic oscillators
is determined in terms of solutions of certain Ermakov and Riccati-type
systems. In addition, we show that the classical Arnold transformation is
naturally connected with Ehrenfest's theorem for generalized harmonic
oscillators.Comment: 10 pages, no figure
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