Question

Explain why the Hamiltonian can be separated into two sets of terms, corresponding to translational energy and internal energy.

Answer 1

Hamiltonian is nothing but the total energy posses by any thing. Like in quantum mechanics, it is the act like an operator resultingly given energy of the system in that eigen state. Similary in statistical or thermodynamical way we said that gas molecules have some internal energy (due to tempreture) and some kinetic energy (translational, vibratrational, rotational energy).

So, in monoatomic gas we can say that hamiltonian is sum of translational energy and internal energy. (monoatomic because it have zero rotational and vibrational degree of freedom)