Quantum Mechanics and the Propagator

Albino Hernández-Galeana, J. M. Rivera-Rebolledo, José Luis López-Bonilla +1 more

Ernesto Flores-González, Hugo Aurelio Morales-Técotl, Juan D. Reyes

We construct the quantum propagator of the free particle in the polymer representation of quantum mechanics, both in position and momentum polarization. We verify the propagator satisfies standard properties such as composition, and that it reduces to the usual Schrödinger propagator in the limit of small parameter μ0, the length scale introduced in the polymer dynamics.

N. Riga, Rebecca Seviour, Kevin L. Jensen +2 more

We present a theoretical study of the correspondence between quantum mechanics (QM) and electromagnetism (EM) using the transfer matrix approach (TMA). This analogy has been studied previously [1] , [2] , [3] ; here we adapt it to electromagnetic wave propagation through an isotropic metamaterial for comparison with quantum tunneling through a one-dimensional barrier. Wigner trajectory calculations for quantum mechanical tunneling have been developed previously [4] , [5] to present a method for modeling electron emission at an atomistic level and to allow for coupling to larger-scale particle-based simulations. To provide a means for computational verification and macroscopic experimental validation of these microscale simulations, we use the TMA to calculate both the QM and EM transmission and reflection coefficients, which enables direct comparison of the respective outputs.