Subatomic degrees of freedom

A third reason is that in actuality the subatomic degrees of freedom result in an expansion of the phase space and an increase of microscopic states. Nevertheless, for the types of system we are interested in here, these contributions are considered constant, only altering the reference state of thermodynamic properties. 

First, from a physical perspective, it is not feasible to account for absolutely all degrees of freedom of a system in calculation of a partition function. Taking into account all subatomic degrees of freedom is impractical. Approximations such as the Born-Oppenheimer approximation that the nucleus of atoms is at the ground state are then indispensable, but the constant contribution to the total partition function is arbitrary. 

The discussion in the preceding section is premised on the assumption that subatomic degrees of freedom are not important for accurate calculation of thermodynamic properties. Naturally, these subatomic degrees of freedom are associated with the state of electrons and nuclei in atoms. In principle, Eq. 7.10 should be modihed to include the nuclear and electronic Hamiltonian... 

Quantum mechanics is the theory that captures the particle-wave duality of matter. Quantum mechanics applies in the microscopic realm, that is, at length scales and at time scales relevant to subatomic particles like electrons and nuclei. It is the most successful physical theory it has been verified by every experiment performed to check its validity. It is iso the most counter-intuitive physical theory, since its premises are at variance with our everyday experience, which is based on macroscopic observations that obey the laws of classical physics. When the properties of physical objects (such as solids, clusters and molecules) are studied at a resolution at which the atomic degrees of freedom are explicitly involved, the use of quantum mechanics becomes necessary. 

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