State reconstruction in one-dimensional quantum mechanics: the continuous spectrum

Ulf Leonhardt, S Schneider

Research output: Contribution to journalArticlepeer-review

18 Citations (Scopus)


We show how to reconstruct the quantum state of one-dimensional wave packets in the continuous part of the spectrum. We assume that the position probability distribution is measured for a sufficiently long time interval and that the potential is known, but otherwise arbitrary. Our paper fills the gap between the tomographic state reconstruction based on free evolution [J. Bertrand and P. Bertrand, Found. Phys. 17, 397 (1987)] and the state determination of moving bound states [U. Leonhardt and M. G. Raymer, Phys. Rev. Lett. 76, 1985 (1996)]. Our result may be relevant with respect to the state determination of atomic beams [Ch. Kurtsiefer, T. Pfau, and J. Mlynek, Nature (London) 386, 150 (1997)] moving in arbitrary potentials.

Original languageEnglish
Pages (from-to)2549-2556
Number of pages8
JournalPhysical Review. A, Atomic, molecular, and optical physics
Publication statusPublished - Oct 1997




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