Abstract
The convenience of coherent state representation is discussed from the viewpoint of what is in a broad sense called the measurement problem in quantum mechanics. Standard quantum theory in coherent state representation is intrinsically related to a number of earlier concepts conciliating quantum and classical processes. From a natural statistical interpretation, free of collapses or measurements, the usual von Neumann-Liiders collapse as well as its quantum state diffusion interpretation follow. In particular, a theory of coupled quantum and classical dynamics arises, containing the fluctuation corrections versus the fenomenological mean-field theories.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
J. von Neumann, Matematische Grundlagen der Quanten Mechanik (Springer, Berlin, 1932).
G. Lüders, Ann. Phys. (Leipzig) 8, 322 (1951).
V. Bargmann, Commun. Pure Appl. Math. 14, 187 (1961). R.J.Glauber, Phys. Rev. 131, 2766 (1963); see also in the recent textbook [4].
D.F. Walls and G.J. Milburn, Quantum Optics (Springer, Berlin, 1994).
A. Lonke, J. Math. Phys. 19, 1110 (1978).
J.S. Bell, Phys. World 3, 33 (1990).
This equation preserves the positivity of ρ(x, p) provided certain analiticity conditions are satisfied initially. It preserves the pure state property of ρ though all forthcoming formulae will be valid for mixtures as well. The proofs will be given elsewhere. The Eq. (10) has an equivalent compact form: On the very right, one may observe the classical Liouville evolution equation to appear in the lowest order of the derivatives.
Full symmetrization (Weyl-ordering) is defined by the recursive rules while
L. Diósi, Quant Semiclass. Opt. 8, 309 (1996). L.Diósi, “A true equation to couple classical and quantum dynamics,” e-print archives quant-ph/9610028.
I.V. Aleksandrov, Z. Naturf. 36A, 902 (1981).
W. Boucher and J. Traschen, Phys. Rev. D 37, 3522 (1988).
Expansion in the derivatives yields the form showing the tricky combination of Liouville’s classical and Schrödinger’s quantum evolutions. The first line of the r.h.s. is identical to the Aleksan-drov-bracket [10] which, in itself, would violate the positivity of ρ [11].
Proofs will be given elsewhere.
N. Gisin and I.C. Percival, J. Phys. A 25, 5677 (1992).
L. Diósi, J. Phys. A 21, 2885 (1988).
Obviously, if the quantum fluctuation of the “current” ĵ is small enough then the last two r.h.s. terms go away. If, furthermore, the states ρc(x, p) and are smooth enough functions of (itx, p) then all r.h.s. terms can be ignored and we are left with the standard mean-field equation
T.N. Sherry and E.C.G. Sudarshan, Phys. Rev. D 18, 4580 (1978).
G.G. de Polavieja, Phys. Lett. 220A, 303 (1996).
L. Diósi, N. Gisin, J. Halliwell, and I.C. Percival, Phys. Rev. Lett. 74, 203 (1995).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1997 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Diósi, L. (1997). Coherent States and the Measurement Problem. In: Ferrero, M., van der Merwe, A. (eds) New Developments on Fundamental Problems in Quantum Physics. Fundamental Theories of Physics, vol 81. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5886-2_15
Download citation
DOI: https://doi.org/10.1007/978-94-011-5886-2_15
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-6487-3
Online ISBN: 978-94-011-5886-2
eBook Packages: Springer Book Archive