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

Stanisław Olszewski^*

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

DOI: 10.4236/jmp.2014.515152                

Abstract

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.

Keywords

Circular Scale of Time, Schrödinger Perturbation Theory, Non-Degenerate Quantum State

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	Schrodinger, E. (1926) Annalen der Physik, 80, 437-490. (in German) http://dx.doi.org/10.1002/andp.19263851302
[2]	Feynman, R.P. (1949) The Physical Review, 76, 749-759. http://dx.doi.org/10.1103/PhysRev.76.749
[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. http://dx.doi.org/10.1088/0370-1328/78/4/306
[5]	Tong, B.Y. (1962) Proceedings of the Physical Society, 80, 1101-1104. http://dx.doi.org/10.1088/0370-1328/80/5/308
[6]	Feynman, R.P. (1966) Science, 153, 699-708. http://dx.doi.org/10.1126/science.153.3737.699
[7]	Olszewski, S. (1991) Zeitschrift für Naturforschung A, 46, 313-320.
[8]	Olszewski, S. and Kwiatkowski, T. (1998) Computers & Chemistry, 22, 445-461. http://dx.doi.org/10.1016/S0097-8485(98)00023-0
[9]	Olszewski, S. (2003) Trends in Physical Chemistry, 9, 69-101.
[10]	Olszewski, S. (2011) Journal of Quantum Information Science, 1, 142-148. http://dx.doi.org/10.4236/jqis.2011.13020
[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. http://dx.doi.org/10.1103/RevModPhys.64.339
[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. http://dx.doi.org/10.4236/jmp.2011.211161
[17]	Olszewski, S. (2012) Journal of Modern Physics, 3, 217-220. http://dx.doi.org/10.4236/jmp.2012.33030
[18]	Olszewski, S. (2012) Quantum Matter, 1, 127-133. http://dx.doi.org/10.1166/qm.2012.1010
[19]	Landau, L.D. and Lifshitz, E.M. (1965) Quantum Mechanics. Pergamon, Oxford.