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TMF, 2011, Volume 168, Number 1, Pages 162–170 (Mi tmf6671)  

This article is cited in 9 scientific papers (total in 9 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: https://doi.org/10.4213/tmf6671

Full text: PDF file (387 kB)
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English version:
Theoretical and Mathematical Physics, 2011, 168:1, 994–1001

Bibliographic databases:


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

    This publication is cited in the following articles:
    1. Nucci M.C., “From Lagrangian to quantum mechanics with symmetries”, Symmetries in Science XV, J. Phys.: Conf. Ser., 380, 2012, 012008  crossref  adsnasa  isi  scopus
    2. Nucci M.C., “Quantizing Preserving Noether Symmetries”, J. Nonlinear Math. Phys., 20:3 (2013), 451–463  crossref  mathscinet  isi  scopus
    3. Nucci M.C., “Symmetries for Thought”, Miskolc Math. Notes, 14:2 (2013), 461–474  mathscinet  zmath  isi
    4. 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  crossref  mathscinet  isi  scopus
    5. Gubbiotti G., Nucci M.C., “Quantization of Quadratic Lienard-Type Equations By Preserving Noether Symmetries”, J. Math. Anal. Appl., 422:2 (2015), 1235–1246  crossref  mathscinet  zmath  isi  scopus
    6. M. C. Nucci, “Ubiquitous symmetries”, Theoret. and Math. Phys., 188:3 (2016), 1361–1370  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    7. Nucci M.C. Sanchini G., “Noether Symmetries Quantization and Superintegrability of Biological Models”, Symmetry-Basel, 8:12 (2016), 155  crossref  mathscinet  isi  scopus
    8. Nucci M.C., “The Nonlinear Pendulum Always Oscillates”, J. Nonlinear Math. Phys., 24:1, SI (2017), 146–156  crossref  mathscinet  isi  scopus
    9. 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  crossref  mathscinet  isi  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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