nt - p h / 07 02 10 7 v 1 1 2 Fe b 20 07 The Quantum Mellin transform
نویسنده
چکیده
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 critial line s = 1/2 − ipη. 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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