Physical Review A
Quantum field theory, Symmetry (Physics), Wave functions
The concept of reciprocity symmetry for matter-wave propagation is established for nonrelativistic quantum mechanics with previous results in the literature extended to include nonlocal interactions. Examples are given for cases with both local and nonlocal potentials, where we show in particular that reciprocity can be violated for the motion of a charged particle in an external electromagnetic field. In addition, this symmetry is applied to interpret a recent analysis [Phys. Rev. A 64, 042716 (2001)] on the symmetry of transmission through one-dimensional complex potentials, with the emphasis that the validity of reciprocity can go beyond that of time-reversal symmetry, such as in the presence of absorption in which the latter symmetry breaks down.
Xie, H. Y., Leung, P. T., & Tsai, D. P. (2008). General validity of reciprocity in quantum mechanics. Physical Review A (Atomic, Molecular, And Optical Physics), 78(6), 064101.