Share This Article:

Circular Scale of Time and Energy of a Quantum State Calculated from the Schrödinger Perturbation Theory

Abstract Full-Text HTML Download Download as PDF (Size:2864KB) PP. 1502-1523
DOI: 10.4236/jmp.2014.515152    2,209 Downloads   2,516 Views   Citations


The main facts about the scale of time considered as a plot of a sequence of events are submitted both to a review and a more detailed calculation. Classical progressive character of the time variable, present in the everyday life and in the modern science, too, is compared with a circular-like kind of advancement of time. This second kind of the time behaviour can be found suitable when a perturbation process of a quantum-mechanical system is examined. In fact the paper demonstrates that the complicated high-order Schrodinger perturbation energy of a non-degenerate quantum state becomes easy to approach of the basis of a circular scale. For example for the perturbation order N = 20 instead of 19! ≈ 1.216 × 1017 Feynman diagrams, the contribution of which should be derived and calculated, only less than 218 ≈ 2.621 × 105 terms belonging to N = 20 should be taken into account to the same purpose.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Olszewski, S. (2014) Circular Scale of Time and Energy of a Quantum State Calculated from the Schrödinger Perturbation Theory. Journal of Modern Physics, 5, 1502-1523. doi: 10.4236/jmp.2014.515152.


[1] Schrodinger, E. (1926) Annalen der Physik, 80, 437-490. (in German)
[2] Feynman, R.P. (1949) The Physical Review, 76, 749-759.
[3] Mattuck, R.D. (1976) A Guide to Feynman Diagrams in a Many-Body Problem. 2nd Edition, McGraw-Hill, New York.
[4] Huby, R. (1961) Proceedings of the Physical Society, 78, 529-536.
[5] Tong, B.Y. (1962) Proceedings of the Physical Society, 80, 1101-1104.
[6] Feynman, R.P. (1966) Science, 153, 699-708.
[7] Olszewski, S. (1991) Zeitschrift für Naturforschung A, 46, 313-320.
[8] Olszewski, S. and Kwiatkowski, T. (1998) Computers & Chemistry, 22, 445-461.
[9] Olszewski, S. (2003) Trends in Physical Chemistry, 9, 69-101.
[10] Olszewski, S. (2011) Journal of Quantum Information Science, 1, 142-148.
[11] Olszewski, S. (2015) Classical Mechanics, Quantum Mechanics and Time Development in the Schrodinger Perturbation Process. Quantum Matter (in Press).
[12] Schommers, W. (1989) Space-Time and Quantum Phenomena. In: Schommers, W., Ed., Quantum Theory and Pictures of Reality, Springer-Verlag, Berlin, 217-277.
[13] Weinberg, S. (2013) Lectures on Quantum Mechanics. Cambridge University Press, Cambridge.
[14] Omnes, R. (1992) Reviews of Modern Physics, 64, 339-382.
[15] Gell-Mann, M. and Hartle, J.B. (1990) In: Zurek, W., Ed., Complexity, Entropy and Physics of Information, Addison-Wesley, Reading.
[16] Olszewski, S. (2011) Journal of Modern Physics, 2, 1305-1309.
[17] Olszewski, S. (2012) Journal of Modern Physics, 3, 217-220.
[18] Olszewski, S. (2012) Quantum Matter, 1, 127-133.
[19] Landau, L.D. and Lifshitz, E.M. (1965) Quantum Mechanics. Pergamon, Oxford.

comments powered by Disqus

Copyright © 2019 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.