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- Avoided_crossing abstract "In quantum physics and quantum chemistry, an avoided crossing (sometimes called intended crossing or non-crossing, anticrossing) is defined as the case when the eigenvalues of a Hermitian matrix representing an observable for a system and depending on N continuous real parameters cannot cross (that is, two or more eigenvalues cannot become equal in value) except at a manifold of N-2 dimensions when the states are symmetric. In the case of a diatomic molecule (one parameter, which describes the bond length), this means that the eigenvalues do not cross. In the case of a triatomic molecule, this means that the eigenvalues can intersect only at a point (see conical intersection).This is particularly important in quantum chemistry. In the Born–Oppenheimer approximation, the electronic molecular Hamiltonian is diagonalized on a set of distinct molecular geometries (the obtained eigenvalues are the values of the adiabatic potential energy surfaces). The geometries for which the potential energy surfaces are avoiding to cross are the locus where the Born–Oppenheimer approximation fails.".
- Avoided_crossing thumbnail Avoided_crossing_in_two-state_system.gif?width=300.
- Avoided_crossing wikiPageID "2174011".
- Avoided_crossing wikiPageRevisionID "599746956".
- Avoided_crossing hasPhotoCollection Avoided_crossing.
- Avoided_crossing subject Category:Quantum_chemistry.
- Avoided_crossing subject Category:Quantum_mechanics.
- Avoided_crossing comment "In quantum physics and quantum chemistry, an avoided crossing (sometimes called intended crossing or non-crossing, anticrossing) is defined as the case when the eigenvalues of a Hermitian matrix representing an observable for a system and depending on N continuous real parameters cannot cross (that is, two or more eigenvalues cannot become equal in value) except at a manifold of N-2 dimensions when the states are symmetric.".
- Avoided_crossing label "Avoided crossing".
- Avoided_crossing label "Croisement évité".
- Avoided_crossing label "Cruce evitado".
- Avoided_crossing label "Cruzamento evitado".
- Avoided_crossing label "Квазипересечение энергетических уровней".
- Avoided_crossing label "擬交差".
- Avoided_crossing sameAs Cruce_evitado.
- Avoided_crossing sameAs Croisement_évité.
- Avoided_crossing sameAs 擬交差.
- Avoided_crossing sameAs Cruzamento_evitado.
- Avoided_crossing sameAs m.06scr8.
- Avoided_crossing sameAs Q2976990.
- Avoided_crossing sameAs Q2976990.
- Avoided_crossing wasDerivedFrom Avoided_crossing?oldid=599746956.
- Avoided_crossing depiction Avoided_crossing_in_two-state_system.gif.
- Avoided_crossing isPrimaryTopicOf Avoided_crossing.
