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Canonical transformation of polynomial hamiltonians

Published online by Cambridge University Press:  17 April 2009

Peter Gavin Lawrence Leach
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Abstract

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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