## Abstract

In Chapter 2 we have discussed the existence and the order of magnitude of quantum effects, showing in particular their importance for microscopic physics. We have seen that quantum effects are relevant for electrons at energies of the order of the electron-Volt, while for the dynamics of atoms in crystals, which have masses three or four order of magnitudes larger, significant effects appear at considerably lower energies, corresponding to low temperatures. Hence, in order to study these effects, a proper theoretical framework is needed for describing systems made up of particles at thermal equilibrium and for deducing their thermodynamical properties from the (quantum) nature of their states.

## Keywords

Partition Function Thermal Equilibrium Occupation Number Single Particle State Grand Canonical Ensemble## Preview

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