Exact Quasi-Classical Asymptotic beyond Maslov Canonical Operator and Quantum Jumps Nature


Exact quasi-classical asymptotic beyond WKB-theory and beyond Maslov canonical operator to the Colombeau solutions of the n-dimensional Schrodinger equation is presented. Quantum jumps nature is considered successfully. We pointed out that an explanation of quantum jumps can be found to result from Colombeau solutions of the Schrodinger equation alone without additional postulates.

Share and Cite:

Foukzon, J. , Potapov, A. and Podosenov, S. (2015) Exact Quasi-Classical Asymptotic beyond Maslov Canonical Operator and Quantum Jumps Nature. Journal of Applied Mathematics and Physics, 3, 584-607. doi: 10.4236/jamp.2015.35072.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] Vijay, R., Slichter, D.H. and Siddiqi, I. (2011) Observation of Quantum Jumps in a Superconducting Artificial Atom. Physical Review Letters, 106, Article ID: 110502.
[2] Peil, S. and Gabrielse, G. (1999) Observing the Quantum Limit of an Electron Cyclotron: QND Measurements of Quantum Jumps between Fock States. Physical Review Letters, 83, 1287-1290.
[3] Sauter, T., Neuhauser, W., Blatt, R. and Toschek, P.E. (1986) Observation of Quantum Jumps. Physical Review Letters, 57, 1696-1698.
[4] Bergquist, J.C., Hulet, R.G., Itano, W.M. and Wineland, D.J. (1986) Observation of Quantum Jumps in a Single Atom. Physical Review Letters, 57, 1699-1702.
[5] Bohr, N. (1913) On the Constitution of Atoms and Molecules. Philosophical Magazine, 26, 1-25.
[6] Dum, R., Zoller, P. and Ritsch, H. (1992) Monte Carlo Simulation of the Atomic Master Equation for Spontaneous Emission. Physical Review A, 45, 4879.
[7] Dalibard, J., Castin, Y. and Mølmer, K. (1992) Wave-Function Approach to Dissipative Processes in Quantum Optics. Physical Review Letters, 68, 580.
[8] Gatarek, D. (1991) Continuous Quantum Jumps and Infinite-Dimensional Stochastic Equations. Journal of Mathematical Physics, 32, 2152-2157.
[9] Molmer, K., Castin, Y. and Dalibard, J. (1993) Monte Carlo Wave-Function Method in Quantum Optics. Journal of the Optical Society of America B, 10, 524-538.
[10] Gardiner, C.W., Parkins, A.S. and Zoller, P. (1992) Wave-Function Quantum Stochastic Differential Equations and Quantum-Jump Simulation Methods. Physical Review A, 46, 4363-4381.
[11] Vogt, N., Jeske, J. and Cole, J.H. (2013) Stochastic Bloch-Redfield Theory: Quantum Jumps in a Solid-Stateenvironment. Physical Review B, 88, Article ID: 174514.
[12] Reiner, J.E., Wiseman, H.M. and Mabuchi, H. (2003) Quantum Jumps between Dressed States: A Proposed Cavity-QED Test Using Feedback. Physical Review A, 67, Article ID: 042106.
[13] Berkeland, D.J., Raymondson, D.A. and Tassin, V.M. (2004) Tests for Non-Randomness in Quantum Jumps. Physical Review A, 69, Article ID: 052103.
[14] Wiseman, H.M. and Milburn, G.J. (1993) Interpretation of Quantum Jump and Diffusion Processes Illustrated on the Bloch Sphere. Physical Review A, 47, 1652-1666.
[15] Wiseman, H.M. and Toombes, G.E. (1999) Quantum Jumps in a Two-Level Atom: Simple Theories versus Quantum Trajectories. Physical Review A, 60, 2474.
[16] Stojanovic, M. (2008) Regularization for Heat Kernel in Nonlinear Parabolic Equations. Taiwanese Journal of Mathematics, 12, 63-87.
[17] Garetto, C. (2008) Fundamental Solutions in the Colombeau Framework: Applications to Solvability and Regularity Theory. Acta Applicandae Mathematicae, 102, 281-318.
[18] Foukzon, J., Potapov, A.A. and Podosenov, S.A. (2011) Exact Quasiclassical Asymptotics beyond Maslov Canonical Operator. International Journal of Recent advances in Physics, 3.
[19] Feynman, E.N. (1964) Integrals and the Schrodinger Equation. Journal of Mathematical Physics, 5, 332-343.
[20] Maslov, V.P. (1976) Complex Markov Cheins and Continual Feynman Integral. Nauka, Moskov.
[21] Apostol, T.M. (1974) Mathematical Analysis. 2nd Edition, Addison-Wesley, Boston.
[22] Chen, W.W.L. (2003) Fundamentals of Analysis. Published by Chen, W.W.L. via Internet.
[23] Gupta, S.L. and Rani, N. (1998) Principles of Real Analysis. Vikas Puplishing House, New Delhi.
[24] Lehmann, J., Reimann, P. and Hanggi, P. (2000) Surmounting Oscillating Barriers: Path-Integral Approach for Weak Noise. Physical Review E, 62, 6282.
[25] Fedoryuk, M.V. (1977) The Method of Steepest Descent. Moscow. (In Russian)
[26] Fedoryuk, M.V. (1989) Asymptotic Methods in Analysis. Encyclopaedia of Mathematical Sciences, 13, 83-191.
[27] Shun, Z. and McCullagh, P. (1995) Laplace Approximation of High Dimensional Integrals. Journal of the Royal Statistical Society: Series B (Methodological), 57, 749-760.
[28] Foukzon, J. (2014) Strong Large Deviations Principles of Non-Freidlin-Wentzell Type-Optimal Control Problem with Imperfect Information—Jumps Phenomena in Financial Markets. Communications in Applied Sciences, 2, 230-363.

Copyright © 2023 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.