The quantum Mellin transform

J. Twamley*, G. J. Milburn

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

28 Citations (Scopus)
6 Downloads (Pure)


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.

Original languageEnglish
Article number328
Pages (from-to)1-20
Number of pages20
JournalNew Journal of Physics
Publication statusPublished - 20 Dec 2006

Bibliographical note

Copyright 2006 IOP Publishing Ltd. Reprinted from New journal of physics. This material is posted here with the permission of IOP Publishing Ltd and the authors. Use of this material is permitted for personal, research and non-commercial uses. Further information regarding the copyright applicable to this article can be viewed at

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