Noether symmetries and the quantization of a Lienard-type nonlinear oscillator
Mathematical Physics
2013-07-16 v1 math.MP
Quantum Physics
Abstract
The classical quantization of a Lienard-type nonlinear oscillator is achieved by a quantization scheme (M.C. Nucci. Theor. Math. Phys., 168:997--1004, 2011) that preserves the Noether point symmetries of the underlying Lagrangian in order to construct the Schr\"odinger equation. This method straightforwardly yields the correct Schr\"odinger equation in the momentum space (V. Chithiika Ruby, M. Senthilvelan, and M. Lakshmanan. J. Phys. A: Math. Gen., 45:382002, 2012), and sheds light into the apparently remarkable connection with the linear harmonic oscillator.
Keywords
Cite
@article{arxiv.1307.3803,
title = {Noether symmetries and the quantization of a Lienard-type nonlinear oscillator},
author = {G. Gubbiotti and M. C. Nucci},
journal= {arXiv preprint arXiv:1307.3803},
year = {2013}
}
Comments
18 pages