The quantum Mellin transform

Twamley, J. and Milburn, G. J. (2006) The quantum Mellin transform. New Journal of Physics, 8 328.1-328.20. doi:10.1088/1367-2630/8/12/328

Author Twamley, J.
Milburn, G. J.
Title The quantum Mellin transform
Journal name New Journal of Physics   Check publisher's open access policy
ISSN 1367-2630
Publication date 2006-12
Sub-type Article (original research)
DOI 10.1088/1367-2630/8/12/328
Open Access Status DOI
Volume 8
Start page 328.1
End page 328.20
Total pages 20
Editor Eberhard Bodenschatz
Place of publication Bristol, United Kingdom
Publisher Institute of Physics Publishing
Collection year 2006
Language eng
Subject C1
249999 Physical Sciences not elsewhere classified
780102 Physical sciences
Formatted abstract
We uncover a new type of unitary operation for quantum mechanics on the half-line which yields a transformation to 'hyperbolic phase space' (η, pη). We show that this new unitary change of basis from the position x on the half line to the hyperbolic momentum pη, transforms the wavef unction via a Mellin transform on to the critical line s = 1 /2 -ipη. We utilize this new transform to find quantum wavefunctions whose hyperbolic momentum representation approximate a class of higher transcendental functions, and in particular, approximate the Riemann-Zeta function. We finally give possible physical realizations to perform an indirect measurement of the hyperbolic momentum of a quantum system on the half-line.
Keyword Physics, multidisciplinary
Degenerate parametric-amplifier
Free particle
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status UQ
Additional Notes Article number 328

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Citation counts: TR Web of Science Citation Count  Cited 20 times in Thomson Reuters Web of Science Article | Citations
Scopus Citation Count Cited 17 times in Scopus Article | Citations
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Created: Wed, 15 Aug 2007, 10:11:28 EST