Question

When is the adiabatic approximation for solid state systems valid?

Answer 1

The adiabatic theorem is a concept in quantum mechanics. Its original form, due to Max Born and Vladimir Fock, was stated as follows:

A physical system remains in its instantaneous eigenstate if a given perturbation is acting on it slowly enough and if there is a gap between the eigenvalueand the rest of the Hamiltonian's spectrum.

In simpler terms, a quantum mechanical system subjected to gradually changing external conditions adapts its functional form, but when subjected to rapidly varying conditions there is insufficient time for the functional form to adapt, so the spatial probability density remains unchanged.

Answer 2

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✔️✔️As it is based on the idea of the nuclii being much heavier than the electrons I would imagine there would be problems for very light atoms like hydrogen.

Also there could occur problems for "heavy electrons" due to the strong curvature is the dispersion relation.

So these two scenarios problems for the adiabatic approximation? Are there more cases it breaks down An furthermore, could you give explicit examples of cases where it breaks down, best with a explanation




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