JMP  Vol.5 No.15 , September 2014
Circular Scale of Time and Energy of a Quantum State Calculated from the Schrödinger Perturbation Theory
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.

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.
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.

 
 
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