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Arrival times in quantum mechanics: Operational and quantum optical approaches
Dissertation zur Erlangung des Doktorgrades der Mathematisch-Naturwissenschaftlichen Fakult¨aten der Georg-August-Universit¨at zu G¨ottingen vorgelegt von Dirk Seidel aus Halle(Saale)
G¨ottingen 2005
D7 Referent: Prof. Dr. G.C. Hegerfeldt Korreferent: Prof. Dr. K. Sch¨onhammer Tag der m¨ undlichen Pr¨ ufung: 06.07.2005
Contents 1 Introduction
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2 Arrival and dwell times in quantum mechanics 2.1 Arrival times . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.1 Classical arrival time . . . . . . . . . . . . . . . . . . . . . . 2.1.2 Quantum arrival times for free motion . . . . . . . . . . . . 2.1.3 Quantum mechanical flux . . . . . . . . . . . . . . . . . . . 2.1.4 Kijowski’s distribution . . . . . . . . . . . . . . . . . . . . . 2.1.5 Aharonov-Bohm arrival-time operator and POVMs . . . . . 2.1.6 Arrival-time distributions and the relation to local densities 2.1.7 Phase times, tunneling times, transmission times . . . . . . 2.2 Dwell times . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.1 Classical dwell time . . . . . . . . . . . . . . . . . . . . . . . 2.2.2 Classical flux-flux correlation function . . . . . . . . . . . . . 2.2.3 Quantum dwell times . . . . . . . . . . . . . . . . . . . . . . 2.2.4 Quantum dwell-time operator . . . . . . . . . . . . . . . . . 2.2.5 Dwell-time distribution for free motion . . . . . . . . . . . . 2.2.6 Moments of the dwell-time distribution . . . . . . . . . . . . 2.2.7 An alternative proposal for free dwell times . . . . . . . . . 3 Operational approaches to quantum arrival times 3.1 The quantum jump approach . . . . . . . . . . . . . . . . . . 3.1.1 Conditional time evolution . . . . . . . . . . . . . . . . 3.1.2 The reset operation and the Bloch equation . . . . . . 3.1.3 Exclusive and non-exclusive