On the Quantum Probability Flux Through Surfaces

We remark that the often ignored quantum probability current is fundamental for a genuine understanding of scattering phenomena and, in particular, for the statistics of the time and position of the first exit of a quantum particle from a given region, which may be simply expressed in terms of the current. This simple formula for these statistics does not appear as such in the literature. It is proposed that the formula, which is very different from the usual quantum mechanical measurement formulas, be verified experimentally. A full understanding of the quantum current and the associated formula is provided by Bohmian mechanics.

[1]  Sheldon Goldstein,et al.  Stochastic mechanics and quantum theory , 1987 .

[2]  D. Dürr,et al.  Scattering and the Role of Operators in Bohmian Mechanics , 1994 .

[3]  Mark S. C. Reed,et al.  Method of Modern Mathematical Physics , 1972 .

[4]  E. Sudarshan,et al.  Zeno's paradox in quantum theory , 1976 .

[5]  V. Enss,et al.  Finite total cross-sections in nonrelativistic quantum mechanics , 1980 .

[6]  Steinberg.  How much time does a tunneling particle spend in the barrier region? , 1995, Physical review letters.

[7]  R. Newton.  Scattering theory of waves and particles , 1966 .

[8]  Lev Vaidman,et al.  Measurement of the Schrödinger Wave of a Single Particle , 1993 .

[9]  Traversal Time for Tunneling , 1982 .

[10]  D. Dürr,et al.  Quantum equilibrium and the origin of absolute uncertainty , 1992, quant-ph/0308039.

[11]  Ph. A. Martin,et al.  Time Delay of Quantum Scattering Processes , 1981 .

[12]  E. B. Davies.  Quantum theory of open systems , 1976 .

[13]  J. Dollard.  Scattering into cones I: Potential scattering , 1969 .

[14]  E. H. Hauge,et al.  Tunneling times: a critical review , 1989 .

[15]  On the flux-across-surfaces theorem , 1995, quant-ph/9511011.

[16]  J. Bell,et al.  Speakable and Unspeakable in Quatum Mechanics , 1988 .

[17]  C. R. Leavens.  Transmission, reflection and dwell times within Bohm's causal interpretation of quantum mechanics , 1990 .

[18]  P. Busch,et al.  The quantum theory of measurement , 1991 .

[19]  Barry Simon,et al.  Quantum Mechanics for Hamiltonians Defined as Quadratic Forms , 1971 .

[20]  Rolf Landauer,et al.  Barrier interaction time in tunneling , 1994 .