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An imaging system is proposed for matter-wave functions that is based onproducing a quadratic phase modulation on the wavefunction of a chargedparticle, analogous to that produced by a space or time lens. The modulation isproduced by co-propagating the wavepacket within an extremum of the harmonicvector and scalar potentials associated with a slow-wave electromagneticstructure. By preceding and following this interaction with appropriatedispersion, characteristic of a solution to the time-dependent Schr\"odingerequation, a system results that is capable of magnifying (i.e., stretching orcompressing the space- and time-scales) and time-reversing an arbitrary quantumwavefunction.

Space-time imaging, magnification and time reversal of matter waves