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EmQM15 – Weak values and the reconstruction problem in Born-Jordan quantization

Maurice de Gosson Related
Physics 24/10/2015

Some time ago Lundeen et al. (Nature 474, 188-99, 2011) have shown how to reconstruct the wavefunction ψ (x) by scanning the weak measurements of the projection operator on x. We show that, more generally, if one works in the Weyl formalism, the post-selected state ψ can easily be reconstructed from the knowledge of the cross-Wigner transform W(ψ,φ) and of the pre-selected state φ (and vice-versa); Lundeen‘s result is then obtained as a particular case of our formula. Mathematical difficulties however occur when one replaces Weyl quantization by the more physical Born-Jordan quantization. We expose some of these difficulties in the presenttalk, and briefly discuss the example of the squared angular momentum.