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Reduced Density Matrices

Luis H. Delgado G.

The standard approach for representing a system in quantum mechanics is to use a wave function. A more power alternative can be obtained using the density matrix formalism.

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Reduction and oxidation (redox) are complementary processes in which one species gains electrons (reduction) and another loses electrons (oxidation). Redox reactions are fundamental in electrochemistry, energy storage, and many biological and inorganic processes; they are often described in terms of oxidation states and half-reactions.

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Runge-Gross Theorem

Michael Rose

The Runge-Gross Theorem is a proof showing that for an electron density evolving in time according to a time-dependent scalar potential, there is a one-to-one mapping between the electron density and that scalar potential. Thus, if we have two systems, with the same initial electron density but evolving according to two distinct time-dependent external potentials, after even an infinitesimally small amount of time has transpired, the resulting densities will no longer be equivalent.

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Reduced Density Matrices

Reduction/Oxidation

Runge-Gross Theorem