Ramsauer-Townsend effect in Shannon and Fisher quantum information entropy, and the uncertainty principle in collision dynamics

Abstract In quantum physics, the scattering of a free particle by an impurity leads to the Ramsauer-Townsend effect, characterized by resonances in the cross section for transmission and reflection of the incident particle. In this work, we analyze this problem within the context of quantum information theory. In particular, we study the Shannon and Fisher entropy, as well as the Heisenberg uncertainty relations, to analyze the fragmentation of a wave packet in collision dynamics. As a primary contribution of this work, we note that these properties are directly related to each other through the same reflection and transmission coefficients as those of the Ramsauer-Townsend effect. Furthermore, we observe that the Heisenberg uncertainty principle satisfies the minimum value, i.e. ℏ /2, for the transmitted wave packet at resonance transmission and a maximum at higher fragmentation of the wave packet. We obtain that at resonance transmission, the reflected contribution to the uncertainty principle is zero with no violation of the Heisenberg principle. This leads, consequently, to the violation of it by the reflected wave packet, as there is no reflection. Moreover, the Shannon and Fisher quantum information entropy is found to be directly connected to Heisenberg’s uncertainty principle for a dynamical system. Finally, we establish that these effects require the proper description of the time-dependent spreading of the wave packet to account for the proper dynamics.