The Quantum Mellin transform
| dc.creator | Twamley, J. | |
| dc.creator | Milburn, G. J. | |
| dc.date | 2007-02-12 | |
| dc.date.accessioned | 2026-07-07T07:46:26Z | |
| dc.date.available | 2026-07-07T07:46:26Z | |
| dc.description | We uncover a new type of unitary operation for quantum mechanics on the half-line which yields a transformation to ``Hyperbolic phase space''. We show that this new unitary change of basis from the position x on the half line to the Hyperbolic momentum $p_η$, transforms the wavefunction via a Mellin transform on to the critial line $s=1/2-ip_η$. We utilise 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 realisations to perform an indirect measurement of the Hyperbolic momentum of a quantum system on the half-line. | |
| dc.description | 23 pages, 6 Figures | |
| dc.identifier | https://arxiv.org/abs/quant-ph/0702107 | |
| dc.identifier | http://arxiv.org/abs/quant-ph/0702107 | |
| dc.identifier | New J Phys 8 328 (2006) | |
| dc.identifier | doi:10.1088/1367-2630/8/12/328 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/123829 | |
| dc.subject | Quantum Physics | |
| dc.title | The Quantum Mellin transform | |
| dc.type | text |