Huygens' principle, the free Schrödinger particle and the quantum anti-centrifugal force

Huygens' principle following from the d'Alembert wave equation is not valid in two-dimensional space. A Schr?dinger particle of vanishing angular momentum moving freely in two dimensions experiences an attractive force - the quantum anti-centrifugal force - towards its centre. 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.