Abstract
Quantal penetration through a (stationary) one-dimensional potential barrier is considered as a time evolution of an initially prepared wave packet. The large-time asymptotics of the process is concerned. Locality of the potential imposes certain analytical properties of the interaction amplitudes in the energy representation. The results are presented in terms of development of the phase-space (Wigner's) quasi-distribution. The phase-space evolution kernel is constructed, and it is shown that in the presence of a positive potential no part of the distribution is transported faster than the free particle. For the case of a small initial momentum uncertainty, the deformation of the coordinate density is considered, including a possible advance of its maximum, which would not mean any noncausal signal transport.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
J. Mehra and H. Rechenberg,The Historical Development of Quantum Theory (Springer-Verlag, New York, 1987) Vol. 5, Part 2, pp. 785 ff.
L. P. Horwitz and I. M. Sigal,Helv. Phys. Acta,51, 685 (1978).
A. Bohm, M. Cadella, and G. B. Mainland,Am. J. Phys. 57, 1103 (1989).
L. P. Horwitz,Found. Phys. 25, 39 (1995).
B. Segev,Classically Forbidden Processes in Quantum Theory, PhD Thesis, Department of Physics, Technion, Haifa, 1996.
C. R. LeavensFound. Phys.,25, 229 (1995).
J. T. Cushing,Found. Phys. 25, 269 (1995).
Proc. of Adriatico Conference “Tunneling and Its Implications” (Trieste, July August 1996), eds. D. Mugnaiet al. (World Scientific, Singapore, to be published).
E. H. Hauge and J. A. StøvnengRev. Mod. Phys. 61, 917 (1989).
R. Landauer and Th. Martin,Rev. Mod. Phys. 66, 217 (1994).
R. J. Eden, P. V. Landshoff, D. I. Olive, and J. C. Polkinghorne,The Analytic S-Matrix (Cambridge University Press, Cambridge, 1966).
N. S. Krylov and V. A. Fock,J. Phys. USSR,11, 112 (1947).
M. S. Marinov and B. Segev,Phys. Rev. A 54, 4752 (1996).
A. Sommerfeld,Partielle Differentialgleichungen der Physik (Harri Deutsch, Thun-Frankfurt, 1978), §28.
M. S. Marinov and B. Segev,J. Phys. A: Math. Gen. 29, 2839 (1996).
E. L. Ince.Ordinary Differential Equations (Dover, New York, 1956), p. 72.
V. DeAlfaro and T. Regge,Potential Scattering (North-Holland, Amsterdam, 1965).
M. L. Goldberger and K. Watson,Collision Theory (Wiley, New York, 1964), Chap. 3.
P. Carruthers and F. Zachariasen,Rev. Mod. Phys. 55, 245 (1983).
E. P. Wigner,Phys. Rev. 98, 145 (1955).
D. W. McLaughlin,J. Math. Phys. 13, 1099 (1072).
D. I. Blokhintsev,The Philosophy of Quantum Mechanics (Reidel, Dordrecht, 1968).
R. Peierls,Surprises in Theoretical Physics (Princeton University Press, Princeton, 1979).
R. Y. Chiao, P. G. Kwiat, and A. M. Steinberg,Sci. Am. 269, August 1993, p. 38.
A. M. Steinberg and R. Y. Chiao,Phys. Rev. A. 49, 3283 (1994).
A. M. Steinberg,Phys. Rev. Lett. 74, 2405 (1995).
A. Ranfagniet al., Phys. Rev. E 48, 1453 (1993).
A. Enders and G. Nimtz,Phys. Rev. B 47, 9605 (1993).
Author information
Authors and Affiliations
Additional information
Supported by G. I. F.
Rights and permissions
About this article
Cite this article
Marinov, M.S., Segev, B. Causality and time dependence in quantum tunneling. Found Phys 27, 113–132 (1997). https://doi.org/10.1007/BF02550160
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02550160