A new approach to quantum backflow
Markus Penz1, Gebhard Grübl1 Sabine Kreidl1 and Peter Wagner2
1Department of Theoretical Physics, University of Innsbruck,
Technikerstr. 25, A-6020 Innsbruck, Austria
2Department of Engineering Mathematics, Geometry and Computer Science,
University of Innsbruck, Technikerstr. 13, A-6020 Innsbruck, Austria
Submitted 11 August 2005, in final form 25 October 2005
Abstract. We derive some rigorous results concerning the backflow operator introduced by Bracken and Melloy. We show that it is linear bounded, self-adjoint and non-compact. Thus the question is underlined whether the backflow constant is an eigenvalue of the backflow operator. From the position representation of the backflow operator, we obtain a more efficient method to determine the backflow constant. Finally, detailed position probability flow properties of a numerical approximation to the (perhaps improper) wavefunction of maximal backflow are displayed.
Published 14 December 2005.
J. Phys. A: Math. Gen. 39, 423 - 433 (2006).
Preprint. http://arXiv.org/abs/quant-ph/0511109, 12 pages, 8 figures, 393 kB.