Schrodinger’s equations of motion

The derivation of the principle of statioiiary action for an atom in a molecule (eqn (8.143)) yields Schrodinger s equation of motion for the total system, identifies the observables of quantum mechanics with the variations of the state function, defines their average values, and gives their equations of motion. We have demonstrated in Chapter 6 how one can use the atomic statement of the principle of stationary action given in eqn (8.148) to derive the theorems of subsystem quantum mechanics and thereby obtain the mechanics of an atom in a molecule. The statement of the atomic action... 

In most circumstances the spatiotemporal dynamics of reacting systems constrained to lie far from equilibrium can be described adequately by reaction-diffusion equations. These equations are valid provided the phenomena of interest occur on distance and time scales that are sufficiently long compared to molecular scales. Naturally, the complete microscopic description of the reacting medium, whether near to or far from equilibrium, must be based on the full molecular dynamics of the system, as embodied in Newton s or Schrodinger s equations of motion. 

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