Abstract
Abstract In this article, I review the methods for calculating vibrational energy levels. To calculate vibrational energy levels, one must choose coordinates, derive a kinetic energy operator, choose basis functions, and compute eigenvalues of a matrix representation of the Hamiltonian operator. All of these components of the calculation are discussed. Iterative methods, in particular the Lanczos method, for obtaining eigenvalues and eigenvectors are stressed. Recent ideas about exploiting symmetry and using contracted basis functions in conjunction with the Lanczos algorithm are presented.
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