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Mathematical Physics Seminar

WEBINAR: Michael Berry - Quantum trajectories: Madelung, de Broglie, Newton…

Location:  Zoom
Date & time: Wednesday, 13 March 2024 at 10:45AM - 11:45AM




Michael Berry – University of Bristol

Wednesday, March 13th, 10:45AM EDT (Zoom meeting starts at 10:30 EDT) 

Quantum trajectories: Madelung, de Broglie, Newton…


The wave counterparts of the classical paths of material particles and the rays of geometrical optics are ‘Madelung trajectories’, modified by a ‘quantum potential’. Wave interference corresponds to undulations in these trajectories, as envisaged by Isaac Newton in his attempts to understand diffraction. The trajectories are strongly influenced by phase singularities (aka wave vortices), with distinctive geometries, contrasting with behaviour at phase saddles. The local quantum velocity (proportional to the phase gradient of the wavefunction), can be faster than the classically allowed speed; this is a generalisation of superoscillations: variations in a bandlimited function that are faster than its largest Fourier frequency. Regions of superoscillation include the phase singularities, and are bounded by manifolds where the quantum potential is zero. The quantum potential suggests a generalisation of quantum mechanics, applicable to classical curl forces, which are not derivable from a potential.

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