The Quantum Statistical Mechanics of a Simple Model System

The Quantum Statistical Mechanics of a Simple Model System... 

The master equation approach has a long story tracing back to the pioneering work of Pauli [6] and van Hove [7], motivated by the need of reconciling quantum mechanical coherence with the evident randomness of statistical physics. In this section we illustrate this transition from coherent to incoherent behavior with a simple, but paradigmatic, model that will be repeatedly adopted in this review. Let us imagine a quantum system with two states, 11) and 2). The incoherent process described by the Pauli master equation is illustrated by the following set of two equations... 

A major success of statistical mechanics is the ability to predict the thermodynamic properties of gases and simple solids from quantum mechanical energy levels. Monatomic gases have translational freedom, which we have treated by using the particle-in-a-box model. Diatomic gases also have vibrational freedom, which we have treated by using the harmonic oscillator model, and rotational freedom, for which we used the rigid-rotor model. The atoms in simple solids can be treated by the Einstein model. More complex systems can require more sophisticated treatments of coupled vibrations or internal rotations or electronic excitations. But these simple models provide a microscopic interpretation of temperature and heat capacity in Chapter 12, and they predict chemical reaction equilibria in Chapter 13, and kinetics in Chapter 19. 

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