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).