Elements of Real Hilbert Spaces Theory

Daniel Sepunaru

RCQCE—Research Center for Quantum Communication Engineering, Holon Academic Institute of Technology, Holon, Israel.

DOI: 10.4236/oalib.1101554                

Abstract

We discuss an alternative version of non-relativistic Newtonian mechanics in terms of real Hilbert space mathematical framework. It is demonstrated that the physics of this scheme is in accordance with the standard formulation. Heisenberg-Schrodinger non-relativistic quantum mechanics is considered adequate and complete. Since the suggested theory is dispersion free, linear superposition principle is not violated but cannot affect results of measurements due to spectral decomposition theorem for self-adjoint operators (the collapse of wave function).

Keywords

Real Hilbert Spaces, Holographic Detection, Quantum Reference Frames

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	Aharonov, Y. and Vaidman, L. (1990) Properties of a Quantum System during the Time Interval between Two Measurements. Physical Review A, 41, 11. http://dx.doi.org/10.1103/PhysRevA.41.11
[2]	von Neumann, J. (1931) Mathematische Grundlagen der Quantenmechanik. Berlin.
[3]	Schrödinger, E. (1935) Die gegenwartige situation in der quantenmechanik. Die Naturwissenschaften, 23, 807, 823, 844.
[4]	Courant, R. and Hilbert, D. (1931) Methoden der Mathematischen Physik. Berlin. http://dx.doi.org/10.1007/978-3-642-47436-1
[5]	von Neumann, J. (1931) über Funktionen von Funktionaloperatoren. Annals of Mathematics, 32.
[6]	Eckart, C. (1926) Operator Calculus and the Solution of the Equation of Quantum Dynamics. Physical Review, 28, 71.
[7]	Schrödinger, E. (1926) Quantizierungals Eigenwert Problem (Erste Mitteilung). Annalen der Physik, 79, 361-376; Schrödinger, E. (1926) Quantizierungals Eigenwert Problem (Zweite Mitteilung). Annalen der Physik, 79, 489-527; Schrödinger, E. (1926) über das Verhältnis der Heisenberg-Born-Jordanschen Quantenmechanikzu der meinen. Annalen der Physik, 79, 734-756; Schrödinger, E. (1926) Quantisierungals Eigenwert Problem (Dritte Mitteilung). Annalen der Physik, 80, 437-490; Schrödinger, E. (1926) Quantisierungals Eigenwert Problem (Vierte Mitteilung). Annalen der Physik, 81, 109-139.
[8]	Tonomura, A., Endo, J., Matsuda, T., Kawasaki, T. and Exawa, H. (1989) Demonstration of Single-Electron Buildup of an Interference Pattern. American Journal of Physics, 57, 117. http://dx.doi.org/10.1119/1.16104
[9]	Carruthers, P. and Nieto, M. (1968) Phase and Angle Variables in Quantum Mechanics. Reviews of Modern Physics, 40, 411. http://dx.doi.org/10.1103/RevModPhys.40.411
[10]	Bouwmeester, D. and Zeilinger, A. (2000) The Physics of Quantum Information. Springer, Berlin. http://dx.doi.org/10.1007/978-3-662-04209-0
[11]	Silverman, M.P. (1995) More than One Mystery. Springer-Verlag, Berlin. http://dx.doi.org/10.1007/978-1-4612-2504-1