Fractional revival of wave packets in an infinite square well: aFourier perspective

Abstract

Fractional revivals of wave packets in an infinite square well arescrutinized with a viewpoint rooted in Fourier analysis, and a compactrelation, expressing the wavefunction Ψ(x,t) for certain values of t interms of spatially displaced copies of Ψ(x,0), is derived withoutappealing to a classical analogy; conditions for the appearance of aninterference pattern in a plot of the position probability density of a wavepacket are deduced, along with related results obtained previously fromdifferent considerations, with minimal effort. The specific case of a packetof Gaussian shape is analysed in greater detail to provide concreteillustrations of fractional revivals with or without interference betweenoverlapping copies of wave packets, depending on whether a finite value of theso-called classical time can or cannot be assigned to the wave packet.