Avoided crossing

Quantum physics and chemistry phenomenon

In quantum physics and quantum chemistry, an avoided crossing is the phenomenon where two eigenvalues of a Hermitian matrix representing a quantum observable and depending on N continuous real parameters cannot become equal in value ("cross") except on a manifold of N-3 dimensions. The phenomenon is also known as the von Neumann–Wigner theorem. In the case of a diatomic molecule, this means that the eigenvalues cannot cross at all. In the case of a triatomic molecule, this means that the eigenvalues can coincide only at a single point.

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