Circular Scale of Time as a Way of Calculating the Quantum-Mechanical Perturbation Energy Given by the Schrödinger Method

Stanisław Olszewski^*

Institute of Physical Chemistry, Polish Academy of Sciences, Warsaw, Poland.

DOI: 10.4236/jqis.2014.44022                

Abstract

The Schrodinger perturbation energy for an arbitrary order N of the perturbation has been presented with the aid of a circular scale of time. The method is of a recurrent character and developed for a non-degenerate quantum state. It allows one to reduce the inflation of terms necessary to calculate known from the Feynman’s diagrammatical approach to a number below that applied in the original Schrodinger perturbation theory.

Keywords

Quantum-Mechanical Perturbation Energy, Circular Scale of Time

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	Jammer, M. (1966) The Conceptual Development of Quantum Mechanics. McGraw-Hill, New York.
[2]	Schrodinger, E. (1926) Quantisierung als Eigenwertproblem, III. Annalen der Physik, 80, 437-490. http://dx.doi.org/10.1002/andp.19263851302
[3]	Feynman, R.P. (1949) The Theory of Positrons. Physical Review, 76, 749-759. http://dx.doi.org/10.1103/PhysRev.76.749
[4]	Mattuck, R.D. (1976) A Guide to Feynman Diagrams in the Many-Body Problem. 2nd Edition, McGraw-Hill, New York.
[5]	Olszewski, S. (1991) Time Scale and Its Application in the Perturbation Theory. Zeitschrift fur Naturforschung, 46A, 313-320.
[6]	Olszewski, S. and Kwiatkowski, T. (1998) A Topological Approach to Evaluation of Non-Degenerate Schrodinger Perturbation Energy Based on a Circular Scale of Time. Computers in Chemistry, 22, 445-461. http://dx.doi.org/10.1016/S0097-8485(98)00023-0
[7]	Olszewski, S. (2003) Two Pathways of the Time Parameter Characteristic for the Perturbation Problem in Quantum Chemistry. Trends in Physical Chemistry, 9, 69-101.
[8]	Slater, J.C. (1960) Quantum Theory of the Atomic Structure, Vol. 1. McGraw-Hill, New York.
[9]	Huby, R. (1961) Formulae for Non-Degenerate Rayleigh-Schrodinger Perturbation Theory in Any Order. Proceedings of the Physical Society (London), 78, 529-536. http://dx.doi.org/10.1088/0370-1328/78/4/306
[10]	Tong, B.Y. (1962) On Huby’s Rules for Non-Degenerate Rayleigh-Schrodinger Perturbation Theory in Any Order. Proceedings of the Physical Society (London), 80, 1101-1104. http://dx.doi.org/10.1088/0370-1328/80/5/308
[11]	Olszewski, S. (2011) Circular Scale of Time Applied in Classifying the Quantum-Mechanical Energy Terms Entering the Framework of the Schrodinger Perturbation Theory. Journal of Quantum Information Science, 1, 142. http://dx.doi.org/10.4236/jqis.2011.13020
[12]	Olszewski, S. (2013) A Look on the Scale of Time Useful in Non-Relativistic Quantum Mechanics. Quantum Matter, 2, 481. http://dx.doi.org/10.1166/qm.2013.1085