Kharkiv Quantum Seminar: February 6, 2024

Quantum trajectories, quantum potential, superoscillations: Madelung, de Broglie, Newton

Michael Berry

 (University of Bristol, Europe)

https://michaelberryphysics.wordpress.com

The wave counterparts of the classical paths of material particles and the rays of geometrical optics are trajectories modified by a ‘quantum potential’. Wave interference corresponds to undulations in these trajectories, as envisaged by Isaac Newton in his attempts to understand what we now understand as diffraction. Trajectories are strongly influenced by phase singularities (aka wave vortices). The local quantum velocity (proportional to the phase gradient of the wavefunction), can be faster than the classically allowed speed. This is an example 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.