Alternative Approach to Time Evaluation of Schrodinger Wave Functions
Author(s)
Mustafa Erol*
Affiliation(s)
Department of Physics Education, Education Faculty of Buca, Dokuz Eylül University, Izmir, Turkey.
Department of Physics Education, Education Faculty of Buca, Dokuz Eylül University, Izmir, Turkey.
ABSTRACT
Time evaluation of wave functions for any quantum mechanical system/particle is essential nevertheless quantum mechanical counterpart of the time dependant classical wave equation does simply not appear. Epistemologically and ontologically considered time dependant momentum operator is initially defined and an Alternative Time Dependant Schrodinger Wave Equation (ATDSWE) is plainly derived. Consequent equation is primarily solved for the free particles, in a closed system, signifying a good agreement with the outcomes of the ordinary TDSWE. Free particle solution interestingly goes further possibly tracing some signs of new pathways to resolve the mysterious quantum world.
Time evaluation of wave functions for any quantum mechanical system/particle is essential nevertheless quantum mechanical counterpart of the time dependant classical wave equation does simply not appear. Epistemologically and ontologically considered time dependant momentum operator is initially defined and an Alternative Time Dependant Schrodinger Wave Equation (ATDSWE) is plainly derived. Consequent equation is primarily solved for the free particles, in a closed system, signifying a good agreement with the outcomes of the ordinary TDSWE. Free particle solution interestingly goes further possibly tracing some signs of new pathways to resolve the mysterious quantum world.
Cite this paper
M. Erol, "Alternative Approach to Time Evaluation of Schrodinger Wave Functions," Journal of Modern Physics, Vol. 3 No. 11, 2012, pp. 1716-1721. doi: 10.4236/jmp.2012.311211.
M. Erol, "Alternative Approach to Time Evaluation of Schrodinger Wave Functions," Journal of Modern Physics, Vol. 3 No. 11, 2012, pp. 1716-1721. doi: 10.4236/jmp.2012.311211.
References
[1] P. A. M. Dirac, “The Principles of Quantum Mechanics,” Oxford University Press, Oxford, 1930. [2] J. von Neumann, “Mathematical Foundations of Quantum Mechanics,” Princeton University Press, Princeton, 1955. [3] R. P. Feyman, R. B. Leighton and M. Sands, “The Feynman Lectures on Physics 1 - 3,” Addison-Wesley, London, 1965. [4] E. Eisberg and R. Resnick, “Quantum Physics of Atoms, Molecules, Solids, Nuclei and Particles,” Wiley and Sons, New York, 1974. [5] R. Penrose, “The Emperor’s New Mind: Concerning Computers, Minds and the Laws of Physics,” Oxford University Press, New York, 1989. [6] D. J. Griffiths, “Introduction to Quantum Mechanics,” Prentice Hall, New York, 2004. [7] A. Einstein, B. Podolski and N. Rosen, “Can Quantum Mechanical Description of Physical Reality Be Considered Complete?” Physical Review, Vol. 47, No. 10, 1935, pp. 777-780. doi:10.1103/PhysRev.47.777 [8] A. Aspect, P. Grangier and G. Roger, “Experimental Realization of Einstein-Podolsky-Rosen-Bohm Gedanken-experiment: A New Violation of Bell’s Inequalities,” Physical Review Letters, Vol. 49, No. 2, 1982, pp. 91-94. doi:10.1103/PhysRevLett.49.91 [9] R. Horodecki, P. Horodecki, M. Horodecki and K. Horodecki, “Quantum Entanglement,” 2009. http://arxiv.org/abs/quant-ph/0702225v2. [10] W. H. Zurek, “Environment-Induced Super Selection Rules,” Physical Review D, Vol. 26, No. 8, 1982, pp. 1862-1880. doi:10.1103/PhysRevD.26.1862 [11] W. H. Zurek, “Decoherence, Einselection and the Quantum Origins of the Classical,” Reviews of Modern Physics, Vol. 75, No. 3, 2003, pp. 715-775. doi:10.1103/RevModPhys.75.715 [12] J. P. Paz and W. H. Zurek, “Environment-Induced Decoherence and the Transition from Quantum to Classical,” In: R. Kaiser, C. Westbrook and F. David, Eds., Coherent Atomic Matter Waves, Les Houches Lectures, Springer, Berlin, 2001, pp. 533-614. [13] B. Misra and E. C. G. Sudarshan, “The Zeno’s Paradox in Quantum Theory,” Journal of Mathematical Physics, Vol. 18, No. 4, 1977, pp. 756-763. doi:10.1063/1.523304 [14] K. Koshino and A. Shimizu, “Quantum Zeno Effect by General Measurements,” Physics Reports, Vol. 412, No. 4, 2005, pp. 191-275. doi:10.1016/j.physrep.2005.03.001 [15] A. Pais, “The Science and Life of Albert Einstein,” Oxford University Press, Oxford, 1982. [16] M. Born, “The Born Einstein Letters,” Walker and Company, New York, 1973. [17] N. Bohr, “Albert Einstein: Philosopher-Scientist,” Cambridge University Press, Cambridge, 1949. [18] M. Rubin, “Locality in the Everett Interpretation of Heisenberg-Picture Quantum Mechanics,” Foundations of Physics Letters, Vol. 14, No. 4, 2001, pp. 301-322. doi:10.1023/A:1012357515678 [19] E. Merzbacher, “Quantum Mechanics,” Wiley International Edition, New York, 1970. [20] H. P. Breuer and F. Petruccione, “The Theory of Open Quantum Systems,” Oxford University Press, New York, 2002. [21] J. G. Muga, R. S. Mayato and I. L. Egusquiza, “Time in Quantum Mechanics,” Springer-Verlag, Heidelberg, 2002. doi:10.1007/3-540-45846-8 [22] R. Penrose, “Shadows of Mind: A Search for the Missing Science of Consciousness”, Oxford University Press, Oxford, 1994. [23] J. Eisert and H. Wiseman, “Quantum Aspects of Life, In Nontrivial Quantum Effects in Biology: A Skeptical Physicists’ View,” World Scientific, Singapore, 2007. [24] H. P. Stapp, “Mind, Matter and Quantum Mechanics,” Springer-Verlag, Berlin-Heidelberg, 2009. doi:10.1007/978-3-540-89654-8 [25] N. Bohr, “The Quantum Postulate and Recent Development of Atomic Theory,” Nature, Vol. 121, No. 3050, 1928, pp. 580-590. doi:10.1038/121580a0 [26] M. Erol, “Quantum Entanglement: Fundamentals and Relations with Consciousness/Mind,” NeuroQuantology, Vol. 8, No. 3, 2010, pp. 390-402. [27] M. Erol, “Schr?dinger Wave Equation and Function: Basics and Concise Relations with Consciousness/Mind,” NeuroQuantology, Vol. 8, No. 1, 2010, pp. 101-109. [28] G. Lindblad, “On the Generators of Quantum Dynamical Semigroups,” Communications in Mathematical Physics, Vol. 48, No. 2, 1976, pp. 119-130. doi:10.1007/BF01608499 [29] S. Attal, A. Joye and C. A. Pillet, “Open Quantum Systems: The Markovian Approach,” Springer, New York, 2006. [30] V. E. Tarasov, “Quantum Mechanics of Non-Hamiltonian and Dissipative Systems,” Elsevier Science, Amsterdam, Boston, London, New York, 2008.
[1] P. A. M. Dirac, “The Principles of Quantum Mechanics,” Oxford University Press, Oxford, 1930. [2] J. von Neumann, “Mathematical Foundations of Quantum Mechanics,” Princeton University Press, Princeton, 1955. [3] R. P. Feyman, R. B. Leighton and M. Sands, “The Feynman Lectures on Physics 1 - 3,” Addison-Wesley, London, 1965. [4] E. Eisberg and R. Resnick, “Quantum Physics of Atoms, Molecules, Solids, Nuclei and Particles,” Wiley and Sons, New York, 1974. [5] R. Penrose, “The Emperor’s New Mind: Concerning Computers, Minds and the Laws of Physics,” Oxford University Press, New York, 1989. [6] D. J. Griffiths, “Introduction to Quantum Mechanics,” Prentice Hall, New York, 2004. [7] A. Einstein, B. Podolski and N. Rosen, “Can Quantum Mechanical Description of Physical Reality Be Considered Complete?” Physical Review, Vol. 47, No. 10, 1935, pp. 777-780. doi:10.1103/PhysRev.47.777 [8] A. Aspect, P. Grangier and G. Roger, “Experimental Realization of Einstein-Podolsky-Rosen-Bohm Gedanken-experiment: A New Violation of Bell’s Inequalities,” Physical Review Letters, Vol. 49, No. 2, 1982, pp. 91-94. doi:10.1103/PhysRevLett.49.91 [9] R. Horodecki, P. Horodecki, M. Horodecki and K. Horodecki, “Quantum Entanglement,” 2009. http://arxiv.org/abs/quant-ph/0702225v2. [10] W. H. Zurek, “Environment-Induced Super Selection Rules,” Physical Review D, Vol. 26, No. 8, 1982, pp. 1862-1880. doi:10.1103/PhysRevD.26.1862 [11] W. H. Zurek, “Decoherence, Einselection and the Quantum Origins of the Classical,” Reviews of Modern Physics, Vol. 75, No. 3, 2003, pp. 715-775. doi:10.1103/RevModPhys.75.715 [12] J. P. Paz and W. H. Zurek, “Environment-Induced Decoherence and the Transition from Quantum to Classical,” In: R. Kaiser, C. Westbrook and F. David, Eds., Coherent Atomic Matter Waves, Les Houches Lectures, Springer, Berlin, 2001, pp. 533-614. [13] B. Misra and E. C. G. Sudarshan, “The Zeno’s Paradox in Quantum Theory,” Journal of Mathematical Physics, Vol. 18, No. 4, 1977, pp. 756-763. doi:10.1063/1.523304 [14] K. Koshino and A. Shimizu, “Quantum Zeno Effect by General Measurements,” Physics Reports, Vol. 412, No. 4, 2005, pp. 191-275. doi:10.1016/j.physrep.2005.03.001 [15] A. Pais, “The Science and Life of Albert Einstein,” Oxford University Press, Oxford, 1982. [16] M. Born, “The Born Einstein Letters,” Walker and Company, New York, 1973. [17] N. Bohr, “Albert Einstein: Philosopher-Scientist,” Cambridge University Press, Cambridge, 1949. [18] M. Rubin, “Locality in the Everett Interpretation of Heisenberg-Picture Quantum Mechanics,” Foundations of Physics Letters, Vol. 14, No. 4, 2001, pp. 301-322. doi:10.1023/A:1012357515678 [19] E. Merzbacher, “Quantum Mechanics,” Wiley International Edition, New York, 1970. [20] H. P. Breuer and F. Petruccione, “The Theory of Open Quantum Systems,” Oxford University Press, New York, 2002. [21] J. G. Muga, R. S. Mayato and I. L. Egusquiza, “Time in Quantum Mechanics,” Springer-Verlag, Heidelberg, 2002. doi:10.1007/3-540-45846-8 [22] R. Penrose, “Shadows of Mind: A Search for the Missing Science of Consciousness”, Oxford University Press, Oxford, 1994. [23] J. Eisert and H. Wiseman, “Quantum Aspects of Life, In Nontrivial Quantum Effects in Biology: A Skeptical Physicists’ View,” World Scientific, Singapore, 2007. [24] H. P. Stapp, “Mind, Matter and Quantum Mechanics,” Springer-Verlag, Berlin-Heidelberg, 2009. doi:10.1007/978-3-540-89654-8 [25] N. Bohr, “The Quantum Postulate and Recent Development of Atomic Theory,” Nature, Vol. 121, No. 3050, 1928, pp. 580-590. doi:10.1038/121580a0 [26] M. Erol, “Quantum Entanglement: Fundamentals and Relations with Consciousness/Mind,” NeuroQuantology, Vol. 8, No. 3, 2010, pp. 390-402. [27] M. Erol, “Schr?dinger Wave Equation and Function: Basics and Concise Relations with Consciousness/Mind,” NeuroQuantology, Vol. 8, No. 1, 2010, pp. 101-109. [28] G. Lindblad, “On the Generators of Quantum Dynamical Semigroups,” Communications in Mathematical Physics, Vol. 48, No. 2, 1976, pp. 119-130. doi:10.1007/BF01608499 [29] S. Attal, A. Joye and C. A. Pillet, “Open Quantum Systems: The Markovian Approach,” Springer, New York, 2006. [30] V. E. Tarasov, “Quantum Mechanics of Non-Hamiltonian and Dissipative Systems,” Elsevier Science, Amsterdam, Boston, London, New York, 2008.