The quantum Mellin transform

Details The quantum Mellin transform The quantum Mellin transform

Dec 2006

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2006njph....8..328t&link_type=abstract

New Journal of Physics, Volume 8, Issue 12, pp. 328 (2006).

Physics

9

Scientific paper

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 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.

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