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20
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84926887574
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T. Wilser, doctoral dissertation, Göttingen, 1991.
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22
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0001183096
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generalizes von Neumann's prescription for observables with nondegenerate eigenvalues to the degenerate case, but differs from von Neumann's proposal for the latter [cf. J. von Neumann, Mathematical Foundations of Quantum Mechanics (Princeton University Press, Princeton, 1955) Chap. V.1].
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(1951)
Ann. Phys. (Leipzig)
, vol.8
, pp. 323
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Lüders, G.1
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28
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84913659322
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edited by, C. DeWitt, A. Blandin, C. Cohen Tannoudji, Gordon and Breach, New York
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(1965)
Les Houches Lectures 1964
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31
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84926924971
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R. Reibold, Physica (to be published); J. Phys. A (to be published).
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47
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84926924970
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This argument neglects a part of the radiation field in the vicinity of the atom.
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48
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84926932886
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uses a similar point of view to determine the reset matrix for a nuclear cascade involving two γ's.
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(1964)
Ann. Phys. (Leipzig)
, vol.14
, pp. 166
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Paul, H.1
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49
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84926905955
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Photon frequencies are not observed, and therefore this detection does not imply restrictions on Δ t. If frequencies were observed also, the time frequency uncertainty relation would apply.
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52
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84926905954
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For the determination of the reset matrix it has been essential that the radiation field is known to have been in the vacuum state a time Δ t before the photon detection. This is due to the gedanken measurements. Without this knowledge it would be much more complicated to determine the state of an atom after the detection because then U(t,0) would enter for larger times. Moreover, since the photon detection times are random a single gedanken measurement before a photon detection would not do.
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54
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84926905952
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Equation ( ref13) should be compared with the expression P0U(t, t0) mid 0ph > mid ψA (t0) > which was calculated in Ref. citePP and whose norm squared gives the probability for a single measurement to find no photon at t, with no measurements, and no knowledge thereof, in between. In principle both expressions are different, e.g., the former decays exponentially while the latter can do this only approximately in some finite interval, not truly asymptotically. This is due to positivity of the energy and ensuing analyticity. As regards the calculation of P0(t), for the external fields considered in Ref. citePP, both results are compatible within the approximations employed. The underlying reason for this agreement has been investigated and clarified in a very general context by means of the projector formalism in Ref. citeRb. However, to find a reset matrix within the approach of Ref. citePP and without gedanken measurements would involve the difficulties mentioned in Ref. citeRem.
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55
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84926944125
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Cf., e.g., D.R. Cox, Renewal Theory (Methuen, London, 1962).
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56
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84926924968
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One can also show direct ly from Eq. ( ref7) that tr hatJ ρA = tr (Hred ρA - ρA Hsup *red).
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