Quantization of quadratic Liénard-type equations by preserving Noether symmetries

Abstract

The classical quantization of a family of a quadratic Liénard-type equation (Liénard II equation) is achieved by a quantization scheme (M.~C. Nucci. {\em 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 as given in (A.~Ghose~Choudhury and Partha Guha. {\em J. Phys. A: Math. Theor.}, 46:165202, 2013).

13 pages. arXiv admin note: text overlap with arXiv:1307.3803 in the Introduction since the authors' method of quantization is described again

References in corpus (3)

• Jacobi's Last Multiplier and Lagrangians for Multidimensional Systems
• An algebraic approach to laying a ghost to rest
• Using an old method of Jacobi to derive Lagrangians: a nonlinear dynamical system with variable coefficients

Cited by in corpus (1)

• On connections of the Liénard equation with some equations of Painlevé--Gambier type