128
Views
2
CrossRef citations to date
0
Altmetric
Articles

Time-independent Hamiltonians describing systems with friction: the “cyclotron with friction”

&
Pages 147-154 | Received 27 Jul 2018, Accepted 15 Sep 2018, Published online: 03 Dec 2018

References

  • Chung-In Um Kyu-Hwang Yeon and George T.F., 2002, The quantum damped harmonic oscillator, Phys. Rep., 362, 63–192. doi: 10.1016/S0370-1573(01)00077-1
  • Levi-Civita T., 1896, Sul moto di un sistema di punti materiali, soggetti a resistenze proporzionali alle rispettive velocità, Atti R. Istit. Veneto Scienze, 54, 1004–1008.
  • Caldirola P., 1941, Forze non conservative nella meccanica quantistica, Nuovo Cimento, 18, 393–400. doi: 10.1007/BF02960144
  • Kanai E., 1948, On the Quantization of the Dissipative Systems Prog. Theor. Phys. 3 440–442. doi: 10.1143/ptp/3.4.440
  • Riewe F., 1996, Nonconservative Lagrangian and Hamiltonian mechanics, Phys. Rev. E, 53, 1890–1899. doi: 10.1103/PhysRevE.53.1890
  • Lemos N.A., 1979, Canonical approach to the damped harmonic oscillator, Amer. J. Phys., 47, 857–858. doi: 10.1119/1.11629
  • Bahar L.Y. and Kwatny H.G., 1981, Generalized Lagrangian and conservation law for the damped harmonic oscillator, Amer. J. Phys., 49, 1062–1065. doi: 10.1119/1.12644
  • Das U., Saha A., Ghosh S. and Talukdar B., 2013, Dissipative systems in a non-dissipative framework, Physica Scripta, 87, Number 6, (2013). doi: 10.1088/0031-8949/87/06/065403
  • Bender C.M., Gianfreda M., Hassanpour N. and Jones H.F., 2016, Comment on “On the Lagrangian and Hamiltonian description of the damped linear harmonic oscillator”, [J. Math. Phys., 48, 032701 (2007)]”, J. Math. Phys., 57, 084101. doi: 10.1063/1.4960722
  • Constantinescu O.A. and Taha E.H., 2017, Alternative Lagrangians obtained by scalar deformations, Preprint, 1712.01392v1 [math.DG].
  • Douglas J., 1941, Solution of the inverse problem of the calculus of variations, Trans. Amer. Math. Soc., 50 (1), 71–128. doi: 10.1090/S0002-9947-1941-0004740-5
  • Sarlet W., 1978, Invariance and conservation laws for Lagrangian systems with one degree of freedom, J. Math. Phys., 19 (5), 1049–1054. doi: 10.1063/1.523767
  • Chandrasekar V.K., Senthilvelan M. and Lakshmanan M., 2007, On the Lagrangian and Hamiltonian description of the damped linear harmonic oscillator, J. Math. Phys., 48, 032701. doi: 10.1063/1.2711375
  • Calogero F. and Françoise J.-P., 2000, Solution of certain integrable dynamical systems of Ruijsenaars–Schneider type with completely periodic trajectories, Ann. Henri Poincaré, 1 173–191. doi: 10.1007/PL00001000
  • Calogero F. and Françoise J.-P., 2000, A novel solvable many-body problem with elliptic interactions, Int. Math. Res. Notices, 15, 775–786. doi: 10.1155/S1073792800000428
  • Degasperis A. and Ruijsenaars S.N.M., 2001, Newton-Equivalent Hamiltonians for the Harmonic Oscillator, Ann. Phys., 293, 92–109. doi: 10.1006/aphy.2001.6169
  • Calogero F. and Graffi S., 2003, On the quantization of a nonlinear Hamiltonian oscillator, Phys. Lett. A, 313, 356–362. doi: 10.1016/S0375-9601(03)00808-9
  • Calogero F., 2003, On the quantization of two other nonlinear harmonic oscillators, Phys. Lett. A, 319, 240–245. doi: 10.1016/j.physleta.2003.10.036
  • Calogero F., 2004, On the quantization of yet another two nonlinear harmonic oscillators, J. Nonlinear Math. Phys., 11, 1–6. doi: 10.2991/jnmp.2004.11.1.1
  • Calogero F. and Degasperis A., 2004, On the quantization of Newton-equivalent Hamiltonians, Amer. J. Phys., 72, 1202–1203. doi: 10.1119/1.1758229
  • Calogero F. and Leyvraz F., “A Hamiltonian yielding damped motion in an homogeneous magnetic field: quantum treatment”, to be published.
  • Calogero F., 2001, The ‘neatest’ many-body problem amenable to exact treatments (a “goldfish”?), Physica D 152–153, 78–84.
  • Calogero F., 2008, Isochronous systems, Oxford University Press (264 pages), paperback edition, 2012.
  • Leyvraz F., 2017, An approach for obtaining integrable Hamiltonians from Poisson-commuting polynomial families, J. Math. Phys., 58, 072902. doi: 10.1063/1.4996581

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.