An Overview on Quantum Trajectories I: Two Bohmian Interpretations

Abstract

The two interpretations of Bohmaian quantum mechanics and their advantage over the standard interpretation are sketched. The Bohmian interpretations rearrange the original mathematical framework of quantum mechanics to expand its physical meaning so that visual intuition on underlying physical processes can be obtained. In particular, the ‘quantum trajectory method' in the hydrodynamical formulation of Madelung-Bohm-Takabayasi quantum mechanics is an example of showing the cognitive importance of scientific illustrations and metaphors in computational quantum chemistry and electrical engineering. The method involves several numerical schemes of solving a set of hydrodynamical equations of motion for the probability density ‘fluids,' based on the propagation of those probability density trajectories. On the other hand, the standard interpretation of quantum mechanics remains to be a probability-based minimalists' approach on a quantum process.