Contracted Schrödinger equation in quantum phase‐space

Abstract

The phase space formulation of quantum mechanics is equivalent to standard quantum mechanics where averages are calculated by way of phase space integration as in the case of classical statistical mechanics. We derive the quantum hierarchy equations, often called the contracted Schrödinger equation, in the phase space representation of quantum mechanics which involves quasi-distributions of position and momentum. We use the Wigner distribution for the phase space function and the Moyal phase space eigenvalue formulation to derive the hierarchy. We show that the hierarchy equations in the position, momentum, and position-momentum representations are very similar in structure. © 2017 Wiley Periodicals, Inc.

Uncover the Hidden Message in DNA

“…DNA has a very straightforward chemistry, giving it major potential for use in nanotechnology (19) in things like nanoscale computers and drug delivery systems. The trouble is that in quantum mechanics the way that wave functions change with time is governed by an equation, the Schrodinger equation (20,21), that does not involve probabilities. It is just as deterministic as Newton's equations of motion and gravitation.…”