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Canonical transformations and their representations in quantum mechanics

Chapter IV. Symplectic Structures — Mechanics

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Part of the Lecture Notes in Mathematics book series (LNM,volume 570)

Keywords

  • Poisson Bracket
  • Canonical Transformation
  • Complex Extension
  • Dimensional Phase Space
  • Linear Canonical Transformation

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References

  1. P.A.M. Dirac, Quantum Mechanics (Clarendon Press, Oxford, Fourth Edition 1958) pp. 103–107.

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  2. M. Moshinsky and C. Quesne, J. Math. Phys. 12, 1772 (1971)

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  3. C. Itzykson, Commun. Math. Phys. 4, 92 (1967)

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  4. V. Bargmann ‘Group Representations on Hilbert Spaces of Analytic Functions’ in Analytic Methods of Mathematical Physics edited by Gilbert and Newton (Gordon & Breach, N.Y. 1968).

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  5. M. Moshinsky, SIAM, J. Appl. Math. 25, 193 (1973).

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  6. J.P. Elliott, Proc. Roy. Soc. London A 245, 128 (1958).

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  7. P. Kramer, M. Moshinsky and T.H. Seligman, ‘Complex Extensions of Canonical Transformations and Quantum Mechanics’ in Group Theory and its Applications Vol. III, edited by E.M. Loebl (Academic Press, New York 1975).

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  8. P.A. Mello and M. Moshinsky, J. Math. Phys. October 1975.

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  9. S.R. de Groot and L.G. Suttorp, Foundations of Electrodynamics (North Holland Publishing Co., Amsterdam 1972) Chapter VI.

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  12. I.S. Gradshteyn and I.W. Ryzhik, Tables of Integrals Series and Products, (Academic Press, New York and London 1965) p. 1039.

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© 1977 Springer-Verlag

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Moshinsky, M. (1977). Canonical transformations and their representations in quantum mechanics. In: Bleuler, K., Reetz, A. (eds) Differential Geometrical Methods in Mathematical Physics. Lecture Notes in Mathematics, vol 570. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0087797

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  • DOI: https://doi.org/10.1007/BFb0087797

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  • Print ISBN: 978-3-540-08068-8

  • Online ISBN: 978-3-540-37498-5

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