The quantum equilibrium distribution tells us the probability for a system to be in a certain configuration at a given time t. That is the basis for the quantum formalism of POVMs, PVMs, and self-adjoint observables on a Hilbert space. In this last chapter we shall return to the beginning of it all, namely to Born’s 1926 papers [1, 2], in which he applies Schrödinger’s wave equation to a scattering situation. In this application, Born recognized the importance of the quantum equilibrium distribution ρ = |ψ|2 as the distribution of the random position of the particle after scattering.
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Reference
M. Born: Z. Phys. 38, 803 (1926)
M. Born: Z. Phys. 37, 863 (1926)
H. Melville: Moby Dick; or, The Whale (William Benton, Encyclopaedia Britanica, Inc., 1952). Greatest Books of the Western World
D. Dürr, S. Teufel: In: Stochastic Processes, Physics and Geometry: New Interplays, I (Leipzig, 1999), CMS Conf. Proc., Vol. 28 (Amer. Math. Soc., Providence, RI, 2000) pp. 123–137
E. Nelson: Dynamical Theories of Brownian Motion (Princeton University Press, Princeton, N.J., 1967)
E. Nelson: Quantum Fluctuations. Princeton Series in Physics (Princeton University Press, Princeton, NJ, 1985)
M. Daumer, D. Dürr, S. Goldstein, N. Zanghì: J. Statist. Phys. 88 (3–4), 967 (1997)
W.O. Amrein, D.B. Pearson: J. Phys. A 30 (15), 5361 (1997)
S. Teufel, D. Dürr, K. Münch-Berndl: J. Math. Phys. 40 (4), 1901 (1999)
D. Dürr, T. Moser, P. Pickl: J. Phys. A 39 (1), 163 (2006)
S. Römer, D. Dürr, T. Moser: J. Phys. A 38, 8421 (2005). Math-ph/0505074
J.D. Dollard: Rocky Mountain J. Math. 1 (1), 5 (1971)
J.D. Dollard, J. Math. Phys. 14 (6), 708 (1973). link.aip.org/link/?JMP/14/708/1
J.M. Combes, R.G. Newton, R. Shtokhamer: Physical Review D 11 (2), 366 (1975)
D. Dürr, S. Teufel: In: Multiscale Methods in Quantum Mechanics: Theory and Experiment, ed. by P. Blanchard, G.F. Dell’Antonio (Birkhäuser, Boston, 2003)
D. Dürr, T. Moser, S. Römer: preprint (2008)
M. Reed, B. Simon: Methods of Modern Mathematical Physics III: Scattering Theory (Academic Press, San Diego, 1979)
P.A. Perry: Scattering Theory by the Enss Method, Mathematical Reports Vol. 1, Part 1 (Harwood academic publishers, New York, 1983)
T. Ikebe: Archive for Rational Mechanics and Analysis 5, 1 (1960)
P. Pickl: J. Math. Phys. 48 (12), 123505, 31 (2007)
P. Pickl, D. Dürr: Commun. Math. Phys. 282 (1), 161 (2008)
E. Merzbacher: Quantum Mechanics, 3rd edn. (John Wiley & Sons, Inc., New York, 1998)
M.L. Goldberger, K.M. Watson: Collision Theory (John Wiley & Sons, Inc., New York, 1964)
D. Dürr, S. Goldstein, T. Moser, N. Zanghü: Commun. Math. Phys. 266 (3), 665 (2006)
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Dürr, D., Teufel, S. (2009). Bohmian Mechanics on Scattering Theory. In: Bohmian Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/b99978_16
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DOI: https://doi.org/10.1007/b99978_16
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