Abstract
The phrase ‘quantum mechanics on phase space’ [1.14] epitomises the fundamental question of the relationship between quantum mechanics and classical mechanics. The deep structural differences between the two theories make it difficult to see how to justify the common claim that the latter theory emerges as an approximation to the former in circumstances under which Planck’s constant can be regarded as small. On the side of the states one would have to explain why superpositions of (vector) states representing macroscopically distinct properties of large systems are practically never observed. We do not enter into this difficult issue here.
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Chapter VI.
E.P. Wigner. On the quantum corrections for thermodynamic equilibrium. Physical Review 40, 749–759, 1932.
J.E. Moyal. Quantum mechanics as a statistical theory. Proceedings of the Cambridge Philosophical Society 45, 99–124, 1949.
J.C.T. Pool. Mathematical aspects of the Weyl correspondence. Journal of Mathematical Physics 7, 66–76, 1966.
K. Husimi. Some formal properties of the density matrix. Proceedings of the Physico—Mathematical Society of Japan 22, 264–314, 1940.
J.R. Klauder, E.C.G. Sudarshan. Fundamentals of Quantum Optics, W.A. Benjamin, New York, 1968.
E. Arthurs, J.L. Kelly. On the simultaneous measurements of a pair of conjugate observables. Bell System Technical Journal 44 725–729, 1965.
P. Busch. Doctoral Thesis, University of Cologne, 1982. English translation: Indeterminacy relations and simultaneous measurements in quantum theory. International Journal of Theoretical Physics 24, 63–92, 1985.
H. Scherer. Doctoral Thesis, University of Cologne, 1994. The part relevant here is published in: H. Scherer, P. Busch. Weakly disturbing phase space measurements in quantum mechanics. In: Quantum Communication and Measurement. Eds. V.P. Belavkin, O. Hirota, R.L. Hudson, Plenum Press, New York, 1995.
Further Reading
E.G. Beltrametti, S. Bugajski. Decomposability of mixed states into pure states and related properties. International Journal of Theoretical Physics 32, 2235–2244, 1993.
S. Bugajski. Nonlinear quantum mechanics is a classical theory. International Journal of Theoretical Physics 30, 961–971, 1991.
P. Busch, P. Lahti, P. Mittelstaedt (EDS.). Symposium on the Foundations of Modern Physics 1993. World Scientific, Singapore, 1993.
Therein
L. Lanz, O. Melsheimer. Quantum mechanics and trajectories, pp. 233–241.
G. Ludwig. The minimal interpretation of quantum mechanics and the objective description of macrosystems, pp. 242–250.
H. Neumann. Macroscopic properties of photon quantum fields, pp. 303–308.
R. Omnès. ¿From Hilbert space to common sense. Annals of Physics 201, 354–447, 1990
M. Singer, W. Stulpe. Phase-space representations of general statistical physical theories. Journal of Mathematical Physics 33, 131–142, 1992.
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(1995). Phase Space. In: Operational Quantum Physics. Lecture Notes in Physics Monographs, vol 31. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-49239-9_6
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DOI: https://doi.org/10.1007/978-3-540-49239-9_6
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