Quantization of quadratic Li\'enard-type equations by preserving Noether symmetries
Abstract
The classical quantization of a family of a quadratic Li\'enard-type equation (Li\'enard II equation) 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 as given in (A.~Ghose~Choudhury and Partha Guha. J. Phys. A: Math. Theor., 46:165202, 2013).
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