This article is cited in 18 papers

Quantization of classical mechanics: Shall we Lie?

M. C. Nucci

Dipartimento di Matematica e Informatica, Università di Perugia, INFN Sezione Perugia, Perugia, Italy

Abstract: We propose a Lie–Noether-symmetry solution of two problems that arise with classical quantization: the quantization of higher-order (more than second) Euler–Lagrange ordinary differential equations of classical mechanics and the quantization of any second-order Euler–Lagrange ordinary differential equation that classically comes from a simple linear equation via nonlinear canonical transformations.

Keywords: quantization, Ostrogradsky method, Schrödinger equation, Lie symmetry, Noether symmetry.

DOI: 10.4213/tmf6671

 English version: Theoretical and Mathematical Physics, 2011, 168:1, 994–1001

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