A method for calculating the eigenvalues of a particle moving in a one‐dimensional potential, given as V(ξ) = υ 1 ξ + υ 2 ξ 2 + υ 3 ξ 3 +… is described. It is a variational method which makes use of linear combinations of H ERMITE orthogonal functions {article}{empty}{document}Φ (ξ) = ∑n = 0N - 1 cₙ uₙ (ξ){document} , the recursion properties of which allow for the calculation of the matrix elements H nm and S nm in closed form without involving any further approximation. As the matrix H = ( H nm ) is a band matrix, the corresponding eigenvalue problem can be solved by applying the LR‐transformation, which yields the eigenvalues in the order of their stability, so that the calculation may be stopped after the required number of the lowest levels has been calculated.
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Heilbronner et al. (1959) studied this question.