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 center. We connect these two phenomena by comparing and contrasting the radial propagators of the d’Alembert wave equation and ...

We investigate theoretically the onset of capillary-gravity waves created by a small object moving at the water-air interface. It is well established that, for straight uniform motion, no steady waves appear at velocities below the minimum phase velocity c(min)=23 cm/s. At higher velocities, the emission of capillary-gravity waves creates an additional drag force. The behavior of this force nea...

For three particles interacting via forces of finite range, it is shown that the wave function interior to the finite volume where all three force ranges overlap completely determines the exterior wave function, provided only the wave functions (half off-shell t matrices) of the isolated two-particle subsystems are also known inside their own range of force. The determination is provided by the...