Abstract
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 wavef unction 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.
| Original language | English |
|---|---|
| Article number | 328 |
| Pages (from-to) | 1-20 |
| Number of pages | 20 |
| Journal | New Journal of Physics |
| Volume | 8 |
| DOIs | |
| Publication status | Published - 20 Dec 2006 |
Bibliographical note
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Cite this
Twamley, J., & Milburn, G. J. (2006). The quantum Mellin transform. New Journal of Physics, 8, 1-20. [328]. https://doi.org/10.1088/1367-2630/8/12/328