Impact of a tunneling particle on the quantum state of a barrier: two-particle wave-packet model

We investigate the scattering of two distinguishable particles with unequal masses and a mutual short-range interaction with the aim of quantifying the impact of a tunneling projectile'' particle on the quantum mechanical state of the barrier’’ particle. We find that the states of the barrier particle after the tunneling or reflection of the projectile are displaced by a finite distance that is given by the derivative of the phase of the transmission or reflection amplitudes multiplied by factors dependent on particles’ masses, respectively. We demonstrate these results on a numerical example with a resonant interaction between a projectile and barrier. Our work demonstrates physical implication of the concept of phase time delay in the form of finite displacements of particles that are, in principle, experimentally measurable.