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S. Olszewski, “Two Pathways of the Time Parameter Characteristic for the Perturbation Problem in Quantum Chemistry,” Trends in Physical Chemistry, Vol. 9, 2003, pp. 69-101.

has been cited by the following article:

• TITLE: Circular Scale of Time Applied in Classifying the Quantum-Mechanical Energy Terms Entering the Framework of the Schrödinger Perturbation Theory

  AUTHORS: S. Olszewski

  KEYWORDS: Circular Scale of Time, Quantum-Mechanical Energy Terms, Complementary Relations, Schrödinger’s Perturbation Theory

  JOURNAL NAME: Journal of Quantum Information Science, Vol.1 No.3, December 9, 2011

  ABSTRACT: The paper applies a one-to-one correspondence which exists between individual Schrödinger perturbation terms and the diagrams obtained on a circular scale of time to whole sets of the Schrödinger terms belonging to a definite perturbation order. In effect the diagram properties allowed us to derive the recurrence formulae giving the number of higher perturbative terms from the number of lower order terms. This recurrence formalism is based on a complementary property that any perturbation order N can be composed of two positive integer components Na , Nb combined into N in all possible ways. Another result concerns the degeneracy of the perturbative terms. This degeneracy is shown to be only twofold and the terms having it are easily detectable on the basis of a circular scale. An analysis of this type demonstrates that the degeneracy of the perturbative terms does not exist for very low perturbative orders. But when the perturbative order exceeds five, the number of degenerate terms predominates heavily over that of nondegenerate terms.