Quantum mechanics on group space and Huygens' principle

Nail H. Ibragimov

Hermann Weyl

M A Cirone, J P Dahl, M Fedorov +2 more

Huygens' principle following from the d'Alembert wave equation is not valid in two-dimensional space. A Schrödinger 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.

M. A. Cirone, Joachim Dahl, Mikhail Vladimirovich Fedorov +2 more

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.

Jörg Bünemann