Bernard, YvesGill, Peter2009-11-012010-12-202009-11-012010-12-20New Journal of Physics 11.083015 (2009)1367-2630http://hdl.handle.net/10440/984http://digitalcollections.anu.edu.au/handle/10440/984The position–momentum dot product (`posmom') s = r·p of a particle is a quantum mechanical observable. In principle, its density S(s) can be derived from the position or momentum wavefunction using Mellin transforms but this leads to complicated integrals and it has therefore been largely neglected by the molecular physics community. However, we show that S(s) can be obtained easily as the Fourier transform of the hyperbolic autocorrelation of the wavefunction. Our findings are illustrated using numerical results for various states of a harmonic oscillator, a hydrogenic ion and particles in a box.15 pageshttp://www.iop.org/EJ/journal/-page=extra.copyright/NJP "NJP’s copyright statement allows authors and their institutions to reproduce, distribute and communicate the published version of their article to the public. Under this agreement NJP authors may: post the published version of their article on their own personal website, on their employer’s website/repository and on free public servers in their subject area." and "Third parties have the same rights to reuse articles in NJP as described in the Creative Commons Attribution-Non-Commercial-ShareAlike 2.5 license. These open access rights allow third-party users to copy, distribute and display the published version of articles in NJP, and create derivative works, subject to appropriate attribution and non-commercial exploitation." - from journal web site (as at 19/02/10)Keywords: Harmonic oscillators; Hydrogenic ion; Mellin transform; Numerical results; Quantum mechanical; Quantum-mechanical system; Wave-functions; Oscillators (electronic); Mathematical transformationsThe distribution of r⋅p in quantum mechanical systems2009-08-1310.1088/1367-2630/11/8/0830152016-02-24