M. C. Nucci, “Quantization of classical mechanics: Shall we Lie?”, TMF, 168:1 (2011), 162–170; Theoret. and Math. Phys., 168:1 (2011), 994

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Teoreticheskaya i Matematicheskaya Fizika, 2011, Volume 168, Number 1, Pages 162–170
DOI: https://doi.org/10.4213/tmf6671 (Mi tmf6671)

This article is cited in 15 scientific papers (total in 15 papers)

Quantization of classical mechanics: Shall we Lie?

M. C. Nucci

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

Full-text PDF (387 kB) Citations (15)

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DOI: https://doi.org/10.4213/tmf6671

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.

English version:
Theoretical and Mathematical Physics, 2011, Volume 168, Issue 1, Pages 994–1001
DOI: https://doi.org/10.1007/s11232-011-0081-3

Bibliographic databases:

Document Type: Article

Language: Russian

Citation: M. C. Nucci, “Quantization of classical mechanics: Shall we Lie?”, TMF, 168:1 (2011), 162–170; Theoret. and Math. Phys., 168:1 (2011), 994–1001

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/tmf6671

https://doi.org/10.4213/tmf6671

https://www.mathnet.ru/eng/tmf/v168/i1/p162

This publication is cited in the following 15 articles:

Maria Clara Nucci, “In search of hidden symmetries”, J. Phys.: Conf. Ser., 2877:1 (2024), 012103
Gabriel González Contreras, Alexander Yakhno, “Symmetries of Systems with the Same Jacobi Multiplier”, Symmetry, 15:7 (2023), 1416
Sinelshchikov D.I., Gaiur I.Yu., Kudryashov N.A., “Lax Representation and Quadratic First Integrals For a Family of Non-Autonomous Second-Order Differential Equations”, J. Math. Anal. Appl., 480:1 (2019), UNSP 123375
Andronikos Paliathanasis, Michael Tsamparlis, “Lie symmetries for systems of evolution equations”, Journal of Geometry and Physics, 124 (2018), 165
Nucci M.C., “The Nonlinear Pendulum Always Oscillates”, J. Nonlinear Math. Phys., 24:1, SI (2017), 146–156
Gubbiotti G. Nucci M.C., “Quantization of the Dynamics of a Particle on a Double Cone By Preserving Noether Symmetries”, J. Nonlinear Math. Phys., 24:3 (2017), 356–367
M. C. Nucci, “Ubiquitous symmetries”, Theoret. and Math. Phys., 188:3 (2016), 1361–1370
Nucci M.C. Sanchini G., “Noether Symmetries Quantization and Superintegrability of Biological Models”, Symmetry-Basel, 8:12 (2016), 155
Gubbiotti G., Nucci M.C., “Quantization of Quadratic Lienard-Type Equations By Preserving Noether Symmetries”, J. Math. Anal. Appl., 422:2 (2015), 1235–1246
M. C. Nucci, “What symmetries can do for you”, Int. J. Mod. Phys. Conf. Ser., 38 (2015), 1560076
Gubbiotti G., Nucci M.C., “Noether Symmetries and the Quantization of a Lienard-Type Nonlinear Oscillator”, J. Nonlinear Math. Phys., 21:2 (2014), 248–264
M C Nucci, “Spectral realization of the Riemann zeros by quantizingH=w(x)(p+ℓ2p/p): the Lie-Noether symmetry approach”, J. Phys.: Conf. Ser., 482 (2014), 012032
Nucci M.C., “Quantizing Preserving Noether Symmetries”, J. Nonlinear Math. Phys., 20:3 (2013), 451–463
Nucci M.C., “Symmetries for Thought”, Miskolc Math. Notes, 14:2 (2013), 461–474
Nucci M.C., “From Lagrangian to quantum mechanics with symmetries”, Symmetries in Science XV, J. Phys.: Conf. Ser., 380, 2012, 012008

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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Abstract page:	550
Full-text PDF :	292
References:	54
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