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Avoided crossing

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In quantum physics and quantum chemistry, an avoided crossing (AC, sometimes called intended crossing, non-crossing or anticrossing) is the phenomenon where two eigenvalues of a Hermitian matrix representing a quantum observable and depending on k {\displaystyle k} continuous real parameters cannot become equal in value ("cross") except on a manifold of dimension k − 2 {\displaystyle k-2} . The phenomenon is also known as the von Neumann–Wigner theorem. In the case of a diatomic molecule (with one parameter, namely the bond length), 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 (see conical intersection).