DETECTION OF SPURIOUS AVOIDED CROSSINGS OF POTENTIAL-ENERGY CURVES

An operator H(λ) may have eigenvalues which cross as a function of the parameter λ. When this operator is represented in terms of its action on the vectors of a certain representation space, the eigenvalues of the representation generally have an avoided crossing. This paper discusses and illustrates the fact that the properties of such a spurious avoided crossing, and the ease with which it may be detected, depend sensitively on the relationship between the representation space and the space spanned by the exact eigenvectors one is trying to represent. © 1979 American Institute of Physics.