Nondispersive accelerating wave packets

Motivated by the work of Berry and Balazs and Greenberger on the 1‐D Schrödinger equation, we have investigated a class of nonspreading solutions to the 3‐D Schrödinger equation involving accelerating Airy envelopes. These solutions are characterized by an asymmetric structure, in contrast to recently derived spherically symmetric packets moving with constant velocities. The field of a characteristic Airy packet extends in an oscillatory fashion behind its peak amplitude, while it quickly disappears in front of the packet’s center. A particle modeled by such a packet seems to leave a wake of its field behind as it accelerates in a certain direction. On the other hand, a wave packet moving with a constant velocity has a field which is symmetrically distributed in all directions. Our work on Airy‐type solutions to the 3‐D Schrödinger equation has led us also to analogous solutions for the 3‐D scalar wave equation.