Huygens' principle, the free Schrodinger particle and the quantum anti-centrifugal force
M. A. Cirone, J. P. Dahl, M. Fedorov, D. Greenberger, W. P. Schleich
Abstract
Huygens' principle following from the d'Alembert wave equation is not valid in two-dimensional space. A Schrodinger particle of vanishing angular momentum moving freely in two dimensions experiences an attractive force - the quantum anti-centrifugal force - towards its center. We connect these two phenomena by comparing and contrasting the radial propagators of the d'Alembert wave equation and of a free non-relativistic quantum mechanical particle in two and three dimensions.
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