The classical quantization of a Li´enard-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¨odinger equation. This method straightforwardly yields the Schr¨odinger 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.

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

NUCCI, Maria Clara
2014

Abstract

The classical quantization of a Li´enard-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¨odinger equation. This method straightforwardly yields the Schr¨odinger 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.
2014
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11391/1221386
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