@article{d504d317ebb54317a833c277aaa08f11,
title = "Exact wave functions for generalized harmonic oscillators",
abstract = "We transform the time-dependent Schr{\"o}dinger 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 the solutions of certain Ermakov and Riccatitype systems. In addition, we show that the classical Arnold transform is naturally connected with Ehrenfest's theorem for generalized harmonic oscillators.",
keywords = "Arnold transform, Ehrenfest theorem, Ermakov-type equation and Pinney-type solution, Green's function, dynamic invariant, generalized harmonic oscillators, time-dependent Schr{\"o}dinger equation",
author = "Nathan Lanfear and L{\'o}pez, {Raquel M.} and Sergei Suslov",
note = "Funding Information: The authors thank Profs. Carlos Castillo-Ch{\'a}vez, Victor V. Dodonov, and Vladimir I. Man{\textquoteright}ko for support, valuable discussions, and encouragement. They are indebted to Dr. Francisco F. L{\'o}pez-Ruiz for kindly pointing out the papers [54, 55] to our attention and for valuable discussions. The authors are grateful to the organizers of the 12th ICSSUR (Foz do Igua¸cu, Brazil, May 02–06, 2011) for their hospitality and an opportunity to present the results of this work. Finally, the authors acknowledge the partial support from the National Science Foundation–Enhancing the Mathematical Sciences Workforce in the 21st Century (EMSW21), award # 0838705, the Alfred P. Sloan Foundation–Sloan National Pipeline Program in the Mathematical and Statistical Sciences, award # LTR 05/19/09, and the National Security Agency–Mathematical & Theoretical Biology Institute—Research program for Undergraduates, award # H98230-09-1-0104.",
year = "2011",
month = jul,
doi = "10.1007/s10946-011-9223-1",
language = "English (US)",
volume = "32",
pages = "352--361",
journal = "Journal of Russian Laser Research",
issn = "1071-2836",
publisher = "Springer New York",
number = "4",
}