Scattering theory from microscopic first principles

Abstract We sketch a derivation of abstract scattering theory from the microscopic first principles defined by Bohmian mechanics. We emphasize the importance of the flux-across-surfaces theorem for the derivation, and of randomness in the impact parameter of the initial wave function — even for an, inevitably inadequate, orthodox derivation.

[1]  The $W^{k,p}$-continuity of wave operators for Schrödinger operators , 1995 .

[2]  W. Amrein,et al.  Flux and scattering into cones for long range and singular potentials , 1997 .

[3]  A. Soffer,et al.  The N-particle scattering problem: asymptotic completeness for short-range systems , 1987 .

[4]  A. Soffer,et al.  Decay estimates for Schrödinger operators , 1991 .

[5]  R. Haag,et al.  Local quantum physics , 1992 .

[6]  Teruo Ikebe,et al.  Eigenfunction expansions associated with the Schroedinger operators and their applications to scattering theory , 1960 .

[7]  On the quantum probability ux through surfaces , 1997 .

[8]  D. Dürr,et al.  The flux-across-surfaces theorem for short range potentials and wave functions without energy cutoffs , 1999 .

[9]  Barry Simon,et al.  Methods of modern mathematical physics. III. Scattering theory , 1979 .

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

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

[12]  D. Bohm A SUGGESTED INTERPRETATION OF THE QUANTUM THEORY IN TERMS OF "HIDDEN" VARIABLES. II , 1952 .

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

[14]  V. Enss Asymptotic completeness for quantum mechanical potential scattering , 1978 .

[15]  P. Perry Scattering theory by the Enss method , 1983 .

[16]  Elspeth Munro,et al.  Summer school. , 1998, Nursing standard (Royal College of Nursing (Great Britain) : 1987).

[17]  K. Berndl,et al.  On the global existence of Bohmian mechanics , 1995, quant-ph/9503013.

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

[19]  Christian Gérard,et al.  Scattering theory of classical and quantum N-particle systems , 1997 .

[20]  S. Goldstein,et al.  On the Quantum Probability Flux Through Surfaces , 1995, quant-ph/9512016.

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

[22]  W. W. Bell Scattering theory in quantum mechanics , 1960 .

[23]  M. Born Quantenmechanik der Stoßvorgänge , 1926 .