dorsal/arxiv
View SchemaThe Quantum Mellin transform
| Authors | J. Twamley, G. J. Milburn |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0702107 |
| URL | https://arxiv.org/abs/quant-ph/0702107 |
| DOI | 10.1088/1367-2630/8/12/328 |
| Journal | New J Phys 8 328 (2006) |
Abstract
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 $p_\eta$, transforms the wavefunction via a Mellin transform on to the critial line $s=1/2-ip_\eta$. 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.
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"abstract": "We uncover a new type of unitary operation for quantum mechanics on the\nhalf-line which yields a transformation to ``Hyperbolic phase space\u0027\u0027. We show\nthat this new unitary change of basis from the position x on the half line to\nthe Hyperbolic momentum $p_\\eta$, transforms the wavefunction via a Mellin\ntransform on to the critial line $s=1/2-ip_\\eta$. We utilise this new transform\nto find quantum wavefunctions whose Hyperbolic momentum representation\napproximate a class of higher transcendental functions, and in particular,\napproximate the Riemann Zeta function. We finally give possible physical\nrealisations to perform an indirect measurement of the Hyperbolic momentum of a\nquantum system on the half-line.",
"arxiv_id": "quant-ph/0702107",
"authors": [
"J. Twamley",
"G. J. Milburn"
],
"categories": [
"quant-ph"
],
"doi": "10.1088/1367-2630/8/12/328",
"journal_ref": "New J Phys 8 328 (2006)",
"title": "The Quantum Mellin transform",
"url": "https://arxiv.org/abs/quant-ph/0702107"
},
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