Title:
Visualization of Topological Structures in Quantum Mechanics and Molecular Physics - Some Deep Connections
Creon Levit
Computational Molecular Nanotechnology Group
NASA Ames Research Center

Abstract:

Normally, both quantum mechanics and chemical physics are difficult to understand without a large investment in their respective vocabularies, mathematics, and underlying assumptions. However, an alternative way of understanding both fields does exist.

The DeBroglie-Bohm-Madelung approach to quantum theory clarifies the understanding of many otherwise counter-intuitive quantum phenomena. Using this theory, there is no need for collapse of the wave function, the mind of the observer, or parallel universes. Instead, by solving relatively simple "quantum-fluid-dynamics" equations, one obtains easy-to-see particle trajectories that obey all of the predictions of standard quantum theory.

Likewise, the approach to theoretical chemistry pioneered by Richard Bader and his students presents a way to visually understand the details of molecular structure and reactivity by using techniques from dynamical systems theory and vector field topology. Viewed in this way, the structure and reactivity of atoms and molecules becomes very clear.

It turns out that the quantum theory of Bohm and the chemical theory of Bader may be equivalent. The topology of the quantum potential elucidates the paradoxes of quantum mechanics, the nature of molecules, the properties of nanoelectronic circuitry, and the structure of the universe.