In classical mechanics we describe a model as:
In quantum mechanics the wave-function is the logical analogue for the trajectory.
We consider models that consist of moving electrons and atomic nuclei (a gas of electrons and atomic nuclei). Any molecule can thus be modeled as a gas of electrons and atomic nuclei and assume the total energy is the sum of :
With this in mind we can write down a general expression for the time independent Schrödinger equation for molecules.
The hamiltonian H for a model with i(1 → N) electrons and A (1 → M ) nulceï is:
Currently it is impossible to find an exact mathematical solution to such a differential equation. Scientists found an approximate solution for the molecular wave-function by using various physical and mathematical principles. In de sequel we explain what you need to understand in order to think up a model and to analyse the calculated results.
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