next up previous
Next: About this document Up: No Title Previous: Concluding Remarks

References

1
Galileo Galilei, "Dialogues Concerning Two New Sciences, Dover Publ., New York 1954

2
Blanchard, Ph. and Jadczyk, A.: Strongly coupled quantum and classical systems and Zeno's effect, Phys. Lett. A 183 (1993) 272--276, and references therein
3
Zeh, H.D.: There are no quantum jumps nor there are particles , Phys. Lett. A 172 (1993) 189--192

4
Ballentine, L.E.: Limitation of the Projection Postulate , Found. Phys 11 (1990) 1329--1343
5
Ballentine, L.E.: Failure of Some Theories of State Reduction , Phys. Rev. A 43 (1991) 9--12
6
Blanchard, Ph., and A. Jadczyk.: Event--Enhanced--Quantum Theory and Piecewise Deterministic Dynamics, Ann. der Physik 4 (1995) 583--599, hep-th 9409189; see also the short version: Event and Piecewise Deterministic Dynamics in Event--Enhanced Quantum Theory , Phys.Lett. A 203 (1995) 260--266
7
Jadczyk, A.: Particle Tracks, Events and Quantum Theory, Progr. Theor. Phys. 93 (1995) 631--646, hep-th/9407157
8
Jadczyk, A.: On Quantum Jumps, Events and Spontaneous Localization Models, Found. Phys. 25 (1995) 743--762, hep-th/9408020
9
Belavkin, V.P., Melsheimer, O.: A Hamiltonian Approach to Quantum Collapse, State Diffusion and Spontaneous Localization , in Quantum Communications and Measurement, Ed. V.P. Belavkin et al, Plenum Press, New York 1995
10
Mott, N.F.: The Wave Mechanics of --Ray Tracks , Proc. Roy. Soc. A 125(1929) 79--884
11
Dicke, R.H.: Interaction--free quantum measurements: A paradox? , Am. J. Phys 49 (1981) 925--930
12
Dicke, R.H.: On Observing the Absence of an Atom , in Between Quantum and Chaos, Ed. Zurek, W. et al., Princeton University Press, Princeton 1988, pp. 400--407
13
Elitzur, A., Vaidman, L.: Quantum Mechanical Interaction--Free Measurements , Found. Phys 23 (1993) 987--997
14
Kwiat, P., Weinfurter, H., Herzog, T, Zeilinger, A.: Interaction--Free Measurement , Phys. Rev. Lett. 74 (1995) 4763--4766
15
Unruh, W.G.: Particles and Fields in Quantum Mechanics in Curved Space--Time, Ed. Audretsch et al, NATO ASI Series B 230, Plenum Press, New York, 1990
16
Bialynicki--Birula, I.: Is Time Sharp or Diffused , in Physical Origins of Time Asymmetry , Ed. Halliwell, J.J. et al., Cambridge University Press 1994
17
Haag, R.: An evolutionary picture for Quantum Physics , to appear, 1996
18
Jauch, J.M.: Foundations of Quantum Mechanics, Addison--Wesley, Reading, Ma. 1968
19
Piron, C.: Foundations of Quantum Physics, W.A. Benjamin, London 1976
20
Dattoli, G., Torre, A., Mignani, R.: Non--Hermitian evolution of two--level quantum systems , Phys. Rev. A 42 (1990) 1467--1475
21
Jost, R.: Bemerkungen zur mathematischen Theorie der Zähler , Helv. Phys. Acta 20 (1947) 173--182
22
Jadczyk, A., Kondrat, G., and Olkiewicz, R.: On uniqueness of the jump process in quantum measurement theory, Preprint BiBoS 711/12/95, quant-ph/9512002
23
Bauch, D.: The Path Integral for a Particle Moving in a -Function Potential , Nuovo Cim. 85 B (1985) 118--123
24
Gaveau, B., and Schulman, L.S.: Explicit time dependent Schrödinger propagators , J. Phys. A 19 (1986) 1833--1846
25
Blinder, S.M.: Green's function and propagator for the one--dimensional --function potential , Phys. Rev. A 37 (1987) 973--976
26
Lavande, S.V. and Bhagwat, K.V.: Feynman propagator for the -function potential , Phys. Lett. A 131 (1988) 8--10
27
Albeverio, S., Gesztesy, F., Høegh--Krohn, R., Holden, H. Solvable Models in Quantum Mechanics, Springer, New York 1988,
28
Manoukian, E.B.: Explicit derivation for a Dirac potential J. Phys. A 22 (1989) 67--70
29
Grosche, C.: Path integrals for potential problems with --function perturbation , J. Phys A 23 (1990) 5205--5234
30
Abramowitz, M., Stegun, I.: Handbook of Mathematical Functions, Dover, New York 1972
31
Brouard, S., Macias, D. and Muga, J.G.: Perfect absorbers for stationary and wavepacket scattering , J. Phys. A 27 (1994) L439--L445
32
Muga, J.G., Brouard, S., and Macias, D.: Time of Arrival in Quantum Mechanics , Ann. Phys. 240 (1995) 351--366
33
Hepp, K.: Quantum Theory of Measurement and Macroscopic Observables , Helv. Phys. Acta 45 (1972) 237--248
34
Wigner, E.P.: Epistemological Perspective on Quantum Theory , in Contemporary Research in the Foundations and Philosophy of Quantum Theory , Hooker (ed.), Reidel Publ. Comp., Dordrecht 1973
35
Weinberg, S.: Testing Quantum Mechanics , Ann. Phys. 194 (1989) 336--386
36
Gisin, N., Rigo, M.: Relevant and irrelevant nonlinear Schrödinger equations , J. Phys. A 28 (1995) 7375--7390
37
Kijowski, J.: On the time operator in quantum mechanics and the Heisenberg uncertainty relation for energy and time , Rep. Math. Phys. 6 (1974) 361--386
38
Allcock, G.R.: The Time Arrival in Quantum Mechanics: I. Formal Considerations , Ann. Phys. 53 (1969) 252--285
39
Mielnik, B.: The Screen Problem , Found. Phys. 24 (1994) 1113--1129
40
Wigner, E.P.: On the Time--Energy Uncertainty Relation , in Aspects of Quantum Theory, Ed. Salam, E., and Wigner, E.P. , Cambridge University Press, Cambridge 1972
41
Recami, E.: A Time Operator and the Time--Energy Uncertainty Relation , in The Uncertainty Principle and Foundations of Quantum Mechanics, Ed. Price, W.C. et al., Wiley, London 1977
42
Pfeifer, P., and Fröhlich, J.: Generalized Time--Energy Uncertainty Relations and Bounds on Life Times Resonances , Preprint ETH-TH/94-31
43
Eisenberg, E., and Horwitz, L.P.: Time, Irreversibility and Unstable Systems in Quantum Physics , Adv. Chem. Phys., to appear
44
Olkhowsky, V.S., and Recami, E.: Recent Developments in the Time Analysis of Tunelling Processes , Phys. Rep. 214 (1992) 339--356
45
Landauer, R.: Barrier interaction time in tunneling , Rev. Mod. Phys. 66 (1994) 217--228
46
Leavens, C.R.: The "tunneling time problem": fundamental incompatibility of the Bohm trajectory approach with the projector and conventional probability current approaches , Phys. Lett. A 197 (1995) 88--94

  
Figure 1: Four shots from the time evolution of a gaussian wavepacket monitored by a gaussian detector placed at the center of the plane. The efficiency of the detector is in this case ca.

  
Figure 2: Probability density of time of arrival for a Dirac's delta counter placed at x=0, coupling constant alpha. The incoming wave packet starts at t=0, x=-4, with velocity v=4

  
Figure 3: Rescaled probability densities of Fig.1

  
Figure 4: Optimal coupling constant as a function of velocity of the incoming wave packet. The dependence pretty soon saturates to a linear one. At the saturation value

  
Figure 5: as a function of for a static wave packet centered over the counter. The maximum, of is reached for

  
Figure 6: as a function of velocity v and coupling constant for a static wave packet centered over the detector.

47
Greenstein, G., Zajonc, A.G.: Do Quantum Jumps Occur at Well Defined Moments of Time? , Am. J. Phys. 63 (1995) 743--745

48
Kärtner, F.X., Haus, H.A.: Quantum--nondemolition measurements and the "collapse of the wave function , Phys. Rev A 47 (1993) 4585--4592

49
Zeh, H.D.: Decoherence and Quantum Measurements , in Stochastic Evolution of Quantum Systems in Open Systems and in Measurement Processes, Ed. L. Diosi and B. Lukacs, World Scientific, Singapore 1994
50
Broyles, A.A.: Nature of Quantum Jumps , Phys. Rev. A 45 (1992) 4925--4931
51
Blanchard, Ph. and Jadczyk, A.: Quantum Mechanics with Event Dynamics, Rep. Math. Phys. 36 No 2/3 (1995), to appear quant-ph/9506014,



Arkadiusz Jadczyk
Thu Feb 22 09:58:31 MET 1996