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Löwdin, P.O. (1966) The Calculation of Upper and Lower Bounds of Energy Eigenvalues in the Perturbation Theory by Means of Partitioning Techniques. In: Wilcox, C.H., Ed., Peturbation Theory and Its Application in Quantum Mechanics, Wiley, New York, 255.

has been cited by the following article:

• TITLE: Circular Scale of Time as a Guide for the Schrödinger Perturbation Process of a Quantum-Mechanical System

  AUTHORS: Stanisław Olszewski

  KEYWORDS: Quantum Mechanics, Schrödinger’s Perturbation Process, Accuracy of a Circular Scale of Time in the Perturbation Calculations

  JOURNAL NAME: World Journal of Mechanics, Vol.9 No.5, May 16, 2019

  ABSTRACT: We point out that a suitable scale of time for the Schrödinger perturbation process is a closed line having rather a circular and not a conventional straight-linear character. A circular nature of the scale concerns especially the time associated with a particular order N of the perturbation energy which provides us with a full number of the perturbation terms predicted by Huby and Tong. On the other hand, a change of the order N—connected with an increased number of the special time points considered on the scale—requires a progressive character of time. A classification of the perturbation terms is done with the aid of the time-point contractions present on a scale characteristic for each N. This selection of terms can be simplified by a partition procedure of the integer numbers representing N-1. The detailed calculations are performed for the perturbation energy of orders N=7 and N=8 .