Effect of approximate linear dependence on the solution of the eigenvalue problem: A study by means of the super-secular equation

✍ Scribed by J. O. Nordling

• Publisher: John Wiley and Sons
• Year: 1975
• Tongue: English
• Weight: 739 KB
• Volume: 9
• Category: Article
• ISSN: 0020-7608
• DOI: 10.1002/qua.560090402

✦ Synopsis

Abstract

Using the super‐secular equation, as defined by Löwdin, this study gives a numerical illustration of the difficulties involved in the solution of the Schrödinger equation with approximate linear dependence in the basis set. The harmonic oscillator is chosen as the model problem and the main part of the study is made for Gaussians as basis set. For comparison some calculations are also reported for another basis set, exponentials. The results show that, with the numerical precision available on present computers, the numerical accuracy for the calculated eigenvalues is critically small also for rather small orders of the basis set—and that the accuracy decreases rapidly with increasing order.