Noether symmetries and the quantization of a Liénard-type nonlinear oscillator

摘要

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 Schr?dinger equation. This method straightforwardly yields the Schr?dinger 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.