Volume 21, Issue 2, March 2014, Pages 248 - 264
Noether symmetries and the quantization of a Liénard-type nonlinear oscillator
Authors
G. Gubbiotti
Dipartimento di Matematica e Fisica Universitá degli Studi Roma Tre Largo San Leonardo Murialdo 1, Pal. C 00146 Roma, Italy,giorgio.gubbiotti@mat.uniroma3.it
M.C. Nucci
Dipartimento di Matematica e Informatica Universitá degli Studi di Perugia & INFN Sezione di Perugia 06123 Perugia, Italy,mariaclara.nucci@unipg.it
Received 13 September 2013, Accepted 21 February 2014, Available Online 6 January 2021.
- DOI
- 10.1080/14029251.2014.905299How to use a DOI?
- Keywords
- Classical quantization; Lie symmetries; Noether symmetries; Liénard-type nonlinear oscillator
- Abstract
The classical quantization of a Liénard-type nonlinear oscillator is achieved by a quantization scheme (M. C. Nucci. Theor. Math. Phys., 168:994–1001, 2011) that preserves the Noether point symmetries of the underlying Lagrangian in order to construct the Schrödinger equation. This method straightforwardly yields the Schrödinger equation in the momentum space as given in (V. Chithiika Ruby, M. Senthilvelan, and M. Lakshmanan. J. Phys. A: Math. Gen., 45:382002, 2012), and sheds light on the apparently remarkable connection with the linear harmonic oscillator.
- Copyright
- © 2014 The Authors. Published by Atlantis Press and Taylor & Francis
- Open Access
- This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).
Cite this article
TY - JOUR AU - G. Gubbiotti AU - M.C. Nucci PY - 2021 DA - 2021/01/06 TI - Noether symmetries and the quantization of a Liénard-type nonlinear oscillator JO - Journal of Nonlinear Mathematical Physics SP - 248 EP - 264 VL - 21 IS - 2 SN - 1776-0852 UR - https://doi.org/10.1080/14029251.2014.905299 DO - 10.1080/14029251.2014.905299 ID - Gubbiotti2021 ER -