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

DOI10.1080/14029251.2014.905299zbMath1421.81038arXiv1307.3803OpenAlexW2964175870MaRDI QIDQ5230946

Maria Clara Nucci, Giorgio Gubbiotti

Publication date: 29 August 2019

Published in: Journal of Nonlinear Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1307.3803

zbMATH Keywords

Lie symmetriesNoether symmetriesclassical quantizationLiénard-type nonlinear oscillator

Mathematics Subject Classification ID

Symmetries, invariants of ordinary differential equations (34C14) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Applications of Lie groups to the sciences; explicit representations (22E70) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Finite-dimensional groups and algebras motivated by physics and their representations (81R05)

Related Items

Factorization technique and isochronous condition for coupled quadratic and mixed Liénard-type nonlinear systems, The inverse problem of a mixed Liénard-type nonlinear oscillator equation from symmetry perspective, Lie point symmetries classification of the mixed Liénard-type equation, Two-dimensional isochronous nonstandard Hamiltonian systems, A note on deriving linearizing transformations for a class of second order nonlinear ordinary differential equations, Quantization of quadratic Liénard-type equations by preserving Noether symmetries, Exact solutions of the Liénard- and generalized Liénard-type ordinary nonlinear differential equations obtained by deforming the phase space coordinates of the linear harmonic oscillator, Ubiquitous symmetries, Quantization of the dynamics of a particle on a double cone by preserving Noether symmetries, The nonlinear pendulum always oscillates, Lax representation and quadratic first integrals for a family of non-autonomous second-order differential equations

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Cites Work

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• Canonical transformations to action and angle variables and their representations in quantum mechanics
• A class of solvable coupled nonlinear oscillators with amplitude independent frequencies
• Lie symmetries, quantisation and \(c\)-isochronous nonlinear oscillators
• Exact quantization of a PT-symmetric (reversible) Liénard-type nonlinear oscillator
• Lagrangians for Dissipative Nonlinear Oscillators: The Method of Jacobi Last Multiplier
• A group theoretical identification of integrable cases of the Liénard-type equation ẍ+f(x)ẋ+g(x)=. I. Equations having nonmaximal number of Lie point symmetries
• An algebraic approach to laying a ghost to rest
• Symmetries of differential equations. IV
• THE LINEAR SYMTRIES OF A NONLINEAR DIFFERENTIAL EQUATION
• Symmetries of linear systems of second-order ordinary differential equations
• The solution of some quantum nonlinear oscillators with the common symmetry groupSL(2,R)
• Wavefunctions for the time-dependent linear oscillator and Lie point symmetries
• On a unique nonlinear oscillator
• Nonlinear canonical transformations in classical and quantum mechanics
• Quantizing preserving Noether symmetries
• A nonlocal connection between certain linear and nonlinear ordinary differential equations/oscillators
• Canonical transformations in quantum mechanics
• Canonical transformations in quantum mechanics
• Lie groups and quantum mechanics