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In the book of Salinas the author says in chapter The Ideal Quantum Gas he says and I quote

The classical models of a gas of diatomic molecules (a rigid rotator in three dimensions, or a rotator with a vibrating axis) are unable to explain the thermal behavior of some quantities, as the specific heat at constant volume. The hamiltonian of a diatomic molecule may be written as a sum of several terms, associated with distinct degrees of freedom, and which do not couple in a first approximation $$\mathcal{H}_{mol} = \mathcal{H}_{translation}+\mathcal{H}_{electronic}+\mathcal{H}_{rotation}+\mathcal{H}_{vibration}+\dots$$

Then I have the following questions.

  1. The justification to maque the sum of the hamiltonians is that the degrees do not interact with one another?
  2. The dots should be used for more degrees of fredom. How many degrees of freedom are in the molecule? There is a spin term and what other degrees? This is a naive question, there are as many terms as we whant to make better and better aproximation to the model?
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  1. Yes. This produces a wavefunction that is product of all the appropriate degrees of freedom.
  2. All the nuclear degrees of freedom come to mind. They are separated from the electronic degrees of freedom in the Born-Oppenheimer approximation so one of the terms not included is $H_{nuclear}$.
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