Hostname: page-component-78c5997874-v9fdk Total loading time: 0 Render date: 2024-11-03T00:12:32.542Z Has data issue: false hasContentIssue false
  • English
  • Français

Canonical transformation of polynomial hamiltonians

Published online by Cambridge University Press:  17 April 2009

Peter Gavin Lawrence Leach
Rights & Permissions [Opens in a new window]

Abstract

An abstract is not available for this content so a preview has been provided. As you have access to this content, a full PDF is available via the ‘Save PDF’ action button.
Image of the first page of this content. For PDF version, please use the ‘Save PDF’ preceeding this image.'
Type
Abstracts of Australasian PhD theses
Information
Bulletin of the Australian Mathematical Society , Volume 19 , Issue 2 , October 1978 , pp. 303 - 306
Copyright
Copyright © Australian Mathematical Society 1979

References

[1]Eliezer, C.J. and Leach, P.G., “The equivalence principle and quantum mechanics”, Amer. J. Phys. 45 (1977), 1218–1221.CrossRefGoogle Scholar
[2]Fradkin, D.M., “Three-dimensional isotropic harmonic oscillator and SU3”, Amer. J. Phys. 33 (1965), 207–211.CrossRefGoogle Scholar
[3]Günther, N.J. and Leach, P.G.L., “Generalized invariants for the time-dependent harmonic oscillator”, J. Mathematical Phys. 18 (1977), 572–576.CrossRefGoogle Scholar
[4]Jauch, J.M. and Hill, E.L., “On the problem of degeneracy in quantum mechanics”, Phys. Rev. 57 (1940), 641–645.CrossRefGoogle Scholar
[5]Leach, P.G.L., “On the theory of time-dependent linear canonical transformations as applied to hamiltonians of the harmonic oscillator type”, J. Mathematical Phys. 18 (1977), 1608–1611.CrossRefGoogle Scholar
[6]Leach, P.G.L., “Invariants and wavefunctions for some time-dependent harmonic oscillator-type hamiltonians”, J. Mathematical Phys. 18 (1977), 1902–1907.CrossRefGoogle Scholar
[7]Leach, P.G.L., “On a direct method for the determination of an exact invariant for the time-dependent harmonic oscillator”, J. Austral. Math. Soc. Ser. B 20 (1977), 97–105.CrossRefGoogle Scholar
[8]Leach, P.G.L., “Quadratic hamiltonians, quadratic invariants and the symmetry group SU(n)”, J. Mathematical Phys. 19 (1978), 446–451.CrossRefGoogle Scholar
[9]Leach, P.G.L., “A note on the time-dependent damped and forced harmonic oscillator”, Amer. J. Phys. (to appear).Google Scholar
[10]Leach, P.G.L., “On non-linear transformations for time-dependent polynomial hamiltonians”, J. Mathematical Phys. (to appear).Google Scholar
[11]Leach, P.G.L., “Towards an invariant for the time-dependent anharmonic oscillator”, J. Mathematical Phys. (to appear).Google Scholar
[12]Leach, P.G.L., “A note on the Hénon-Heiles problem”, J. Mathematical Phys. (to appear).Google Scholar
[13]Leach, P.G.L., “Quadratic hamiltonians: the four classes of quadratic invariants, their interrelations and symmetries”, submitted.Google Scholar
[14]Lewis, H.R. Jr, “Classical and quantum systems with time-dependent harmonic-oscillator-type hamiltonians”, Phys. Rev. Lett. 18 (1967), 510–512.CrossRefGoogle Scholar
[15]Lewis, H.R. Jr, “Motion of a time-dependent harmonic oscillator, and of a charged particle in a class of time-dependent, axially symmetric electromagnetic fields”, Phys. Rev. 172 (1968), 1313–1315.CrossRefGoogle Scholar
[16]Lewis, H.R. Jr, “Class of exact invariants for classical and quantum time-dependent harmonic oscillators”, J. Mathematical Phys. 9 (1968), 1976–1986.CrossRefGoogle Scholar
[17]Lewis, H.R. Jr and Riesenfield, W.B., “An exact quantum theory of the time-dependent harmonic oscillator and of a charged particle in a time-dependent electromagnetic field”, J. Mathematical Phys. 10 (1969), 1458–1473.CrossRefGoogle Scholar