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- Avoided_crossing abstract "In quantum physics and quantum chemistry, an avoided crossing (sometimes called intended crossing, non-crossing or anticrossing) is defined as the case when the eigenvalues of an 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 wikiPageLength "14146".
- Avoided_crossing wikiPageOutDegree "42".
- Avoided_crossing wikiPageRevisionID "680279831".
- Avoided_crossing wikiPageWikiLink Adiabatic.
- Avoided_crossing wikiPageWikiLink Adiabatic_process.
- Avoided_crossing wikiPageWikiLink Adiabatic_theorem.
- Avoided_crossing wikiPageWikiLink Benzene.
- Avoided_crossing wikiPageWikiLink Bond_hardening.
- Avoided_crossing wikiPageWikiLink Bond_length.
- Avoided_crossing wikiPageWikiLink Bond_softening.
- Avoided_crossing wikiPageWikiLink Born–Oppenheimer_approximation.
- Avoided_crossing wikiPageWikiLink Bra–ket.
- Avoided_crossing wikiPageWikiLink Category:Quantum_chemistry.
- Avoided_crossing wikiPageWikiLink Category:Quantum_mechanics.
- Avoided_crossing wikiPageWikiLink Co-ordinates.
- Avoided_crossing wikiPageWikiLink Conical_intersection.
- Avoided_crossing wikiPageWikiLink Coordinate_system.
- Avoided_crossing wikiPageWikiLink Degeneracy_(quantum_mechanics).
- Avoided_crossing wikiPageWikiLink Degenerate_energy_levels.
- Avoided_crossing wikiPageWikiLink Diagonalizable_matrix.
- Avoided_crossing wikiPageWikiLink Diatomic.
- Avoided_crossing wikiPageWikiLink Diatomic_molecule.
- Avoided_crossing wikiPageWikiLink Eigenvalue.
- Avoided_crossing wikiPageWikiLink Eigenvalues_and_eigenvectors.
- Avoided_crossing wikiPageWikiLink Eigenvector.
- Avoided_crossing wikiPageWikiLink Electronic_molecular_Hamiltonian.
- Avoided_crossing wikiPageWikiLink Hamiltonian_(quantum_mechanics).
- Avoided_crossing wikiPageWikiLink Hermitian_matrix.
- Avoided_crossing wikiPageWikiLink Landau–Zener_formula.
- Avoided_crossing wikiPageWikiLink Level_repulsion.
- Avoided_crossing wikiPageWikiLink Linear_subspace.
- Avoided_crossing wikiPageWikiLink Locus_(mathematics).
- Avoided_crossing wikiPageWikiLink Manifold.
- Avoided_crossing wikiPageWikiLink Molecular_Hamiltonian.
- Avoided_crossing wikiPageWikiLink Parametrization.
- Avoided_crossing wikiPageWikiLink Perturbation_theory_(quantum_mechanics).
- Avoided_crossing wikiPageWikiLink Physical_system.
- Avoided_crossing wikiPageWikiLink Potential_energy_surface.
- Avoided_crossing wikiPageWikiLink Quantum_chemistry.
- Avoided_crossing wikiPageWikiLink Quantum_mechanics.
- Avoided_crossing wikiPageWikiLink Quantum_physics.
- Avoided_crossing wikiPageWikiLink Quantum_system.
- Avoided_crossing wikiPageWikiLink Resonance_(chemistry).
- Avoided_crossing wikiPageWikiLink Surface.
- Avoided_crossing wikiPageWikiLink Two-level_system.
- Avoided_crossing wikiPageWikiLink Two-state_quantum_system.
- Avoided_crossing wikiPageWikiLink File:Avoided_crossing_in_two-state_system.gif.
- Avoided_crossing wikiPageWikiLink File:Benzene_delocalization.svg.
- Avoided_crossing wikiPageWikiLinkText "Avoided crossing".
- Avoided_crossing wikiPageWikiLinkText "Avoided_crossing".
- Avoided_crossing wikiPageWikiLinkText "Curve crossing".
- Avoided_crossing wikiPageWikiLinkText "Wigner–von Neumann non-crossing".
- Avoided_crossing wikiPageWikiLinkText "anticrossing".
- Avoided_crossing wikiPageWikiLinkText "avoided crossing rule".
- Avoided_crossing wikiPageWikiLinkText "avoided crossing".
- Avoided_crossing wikiPageWikiLinkText "avoided crossings".
- Avoided_crossing wikiPageWikiLinkText "avoided level crossing".
- Avoided_crossing wikiPageWikiLinkText "level crossing".
- Avoided_crossing wikiPageWikiLinkText "turn into anticrossings".
- Avoided_crossing hasPhotoCollection Avoided_crossing.
- Avoided_crossing wikiPageUsesTemplate Template:Reflist.
- Avoided_crossing subject Category:Quantum_chemistry.
- Avoided_crossing subject Category:Quantum_mechanics.
- Avoided_crossing type Mechanic.
- Avoided_crossing comment "In quantum physics and quantum chemistry, an avoided crossing (sometimes called intended crossing, non-crossing or anticrossing) is defined as the case when the eigenvalues of an 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 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 Квазипересечение_энергетических_уровней.
- Avoided_crossing sameAs Q2976990.
- Avoided_crossing sameAs Q2976990.
- Avoided_crossing wasDerivedFrom Avoided_crossing?oldid=680279831.
- Avoided_crossing depiction Avoided_crossing_in_two-state_system.gif.
- Avoided_crossing isPrimaryTopicOf Avoided_crossing.