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In quantum physics and quantum chemistry, an avoided crossing (AC, sometimes called intended crossing, [1] non-crossing or anticrossing) is the phenomenon where two eigenvalues of a Hermitian matrix representing a quantum observable and depending on continuous real parameters cannot become equal in value ("cross") except on a manifold of dimension . [2]
Sketch of an avoided crossing.The graph represents the energies of the system along a parameter z (which may be vary in time). The dashed lines represent the energies of the diabatic states, which cross each other at z c, and the full lines represent the energy of the adiabatic states (eigenvalues of the Hamiltonian).
Ideal Conical Intersection. In quantum chemistry, a conical intersection of two or more potential energy surfaces is the set of molecular geometry points where the potential energy surfaces are degenerate (intersect) and the non-adiabatic couplings between these states are non-vanishing.
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Nearby an avoided crossing or conical intersection, these terms are substantive. Therefore one unitary transformation is performed from the adiabatic representation to the so-called diabatic representation in which the nuclear kinetic energy operator is diagonal.
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Avoided crossing; Intersubband polariton; Wigner–Ville distribution; References This page was last edited on 23 October 2020, at 19:09 (UTC). Text is ...