Please use this identifier to cite or link to this item: http://hdl.handle.net/1959.14/38411
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- Title
- The Quantum Mellin transform
- Related
- New journal of physics, Vol. 8, Issue 12, Article No. 328,
- DOI
- 10.1088/1367-2630/8/12/328
- Publisher
- Institute of Physics Publishing
- Date
- 2006
- FoR/RFCD Code(s)
-
010503 Mathematical Aspects of Classical Mechanics, Quantum Mechanics and Quantum Information Theory
020602 Field Theory and String Theory
- Author/Creator
- Twamley, J
- Author/Creator
- Milburn, G. J
- Description
- 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 χ on the half line to the hyperbolic momentum pη, transforms the wavefunction 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.
- Description
- 20 page(s)
- Subject Keyword
- 010503 Mathematical Aspects of Classical Mechanics, Quantum Mechanics and Quantum Information Theory
- Subject Keyword
- 020602 Field Theory and String Theory
- Resource Type
- journal article
- Organisation
- Macquarie University. Centre for Quantum Computer Technology
- Organisation
- Macquarie University. Dept. of Physics
- Identifier
- http://hdl.handle.net/1959.14/38411
- Identifier
- ISSN:1367-2630
- Identifier
- mq-rm-2006005449
- Language
- eng
- Rights
- 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 http://www.iop.org/EJ/journal/-page=extra.copyright/NJP.
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