The eigenvalue problem of the one-dimensional potential well V (X) =a‖X‖ is solved by means of certain higher-order phase-integral approximations. The purpose of this paper is to demonstrate numerically the applicability and accuracy of these approximations (which are related to, but not identical to, the higher-order JWKB approximations) and, therefore, a comparison is made with exact results. An upper bound for the absolute error in the first-order approximation is calculated analytically and found to be in accordance with the actual numerical results which are displayed in a table.
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B. Thidé (1976) studied this question.