Article | REF: AF110 V1

Separation and contraction of variables in molecular spectroscopy

Author: Patrick CASSAM-CHENAÏ

Publication date: April 10, 2014, Review date: April 26, 2021

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2. Separation of variables in a molecular system

We've just outlined the theoretical framework we need to describe molecular quantum physics. We will now implement it to calculate the energy levels of a molecule. As a first step, we'll try to simplify the approach, by separating the degrees of freedom of the molecular system, in accordance with Descartes' second precept: "to divide each of the difficulties I examine, into as many parcels as it is possible and necessary to solve them better". Wherever this results in an approximation, we will emphasize the limits of the description.

2.1 Separation of time variable

We will restrict ourselves to the case, which is not very restrictive in molecular spectroscopy, where the Hamiltonian can be chosen to be independent of time. As we have seen, in this case the Hamiltonian...

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Separation of variables in a molecular system