The quantum Mellin transform

J. Twamley*, G. J. Milburn

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    39 Citations (Scopus)
    31 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


    Dive into the research topics of 'The quantum Mellin transform'. Together they form a unique fingerprint.

    Cite this