On the Physical Representation of Quantum Systems
( Pp. 13-18)
Abstract:
The Schrödinger equation for bound states depends on a second derivative, that only exists if the solution is continuous, which is - by itself - contradictory, and cannot be digitally calculated. Photons can be created in-phase by stimulated emission or annihilated by spontaneous absorption, and break the LEM, more likely at lower frequencies, and even in vacuum. Thus, the number of particles is not conserved, e.g., in the double-slit experiment, even at low-light intensity. Physical representations of quantum computation (QC), cannot, thus, follow some customarily assumed aspects of quantum mechanics. This is solved by considering the Schrödinger equation depending on the curvature, which is expressed exactly as a difference equation, works for any wavelength, and is variationally solved for natural numbers, representing naturally the quantum energy levels. This leads to accepting both forms in a universality model. Further, one follows the Bohr model in QC, in a software-defined QC, where GF(2m) can be used with binary logic to implement in software Bohr’s idea of “many states at once”, without breaking the LEM, in the macro, without necessarily using special hardware (e.g. quantum annealing), or incurring in decoherence, designed with today’s binary computers, even a cell phone.
How to Cite:
Gerck E.., (2021), ON THE PHYSICAL REPRESENTATION OF QUANTUM SYSTEMS. Computational Nanotechnology, 3 => 13-18.
Reference list:
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Gerck E., d Oliveira A.B. Continued fraction calculation of the eigen-values of tridiagonal matrices arising from the Schr dinger equation. Journal of Computational and Applied Mathematics. 1980. No. 6 (1). Pp. 81-82. Copy online at https://www.researchgate.net/publication/242978992/
Gerck E., Gallas J.A.C., d Oliveira A.B. Solution of the Schr dinger equation for bound states in closed form. Physical Review. 1982. No. A 26. P. 1 (1).
Gerck E., d Oliveira A.B., Gallas J.A.C. New approach to calculate bound state eigenvalues. Revista Brasileira de Ensino de Fisica. 1983. No. 13 (1). Pp. 183-300.
Ozhigov Y.I. Constructive physics (physics research and technology). Ed. UK: Nova Science Pub. Inc, 2011. ISBN 1612095534.
Wilson K.G. The renormalization group: Critical phenomena and the Kondo problem. J. Physique Lett. 1975. No. 43. Pp. 211-216,
Gerck E. The exponential difference. Private communication, cited in report number: EAV-12/78. Laboratorio de Estudos Avancados, IAE, CTA, Brazil: S.J. Campos, SP, 1978. Copy online at https://www.researchgate.net/publication/286625459/
Gerck E., Miranda L. Quantum well lasers tunable by long wavelength radiation. Applied Physics Letters. 1984. No. 44 (9). Pp. 837-839.
Ahlfors L. Complex analysis. McGraw-Hill, Inc., 1979.
Havil J. The irrationals. Princeton University Press, 2012.
Khrennikov A.Y. Universality in network dynamics. Springer Science Business Media. 2013. Vol. 427.
Schr dinger E. Collected papers on wave mechanics. International Series of Monographs on Physics. Book 27. Clarendon Pess, 1982.
Bouwmeester D. The physics of quantum information: Quantum cryptography, quantum teleportation, quantum computation. A. Ekert, A. Zeilinger (eds.). Springer Publishing Company, Incorporated, 2010.
Gerck E. Presentation: Tri-State (or more) quantum information model. Quantum Informatics 2021. Faculty of Computational Mathematics and Cybernetics of Lomonosov Moscow State University. 2021. Current, longer version at https://www.researchgate.net/publication/347563918/
Einstein A. Strahlungs-Emission und Absorption nach der Quantentheorie. Deutsche Physikalische Gesellschaft. Jan. 1916. Vol. 18. Pp. 318-323,
Einstein A. Zur Quantentheorie der Strahlung. Physikalische Zeitschrift. Jan. 1917. Vol. 18. Pp. 121-128,
Petersen A. The philosophy of Niels Bohr. Bulletin of the Atomic Scientists. 1963. Vol. 19. No. 7.
Grib A., Rodrigues W.A.Jr. Copenhagen interpretation. In: Nonlocality in quantum physics. Boston, MA: Springer, 1999. https://doi.Org/10.1007/978-1-4615-4687-0.5
Howard D. Who invented the copenhagen interpretation A study in mythology. Philosophy of Science. 2004. Vol. 71. No. 5. Pp. 669-682.
Gerck E. Presentation: On the physical representation of quantum systems. Quantum Informatics 2021. Faculty of Computational Mathematics and Cybernetics of Lomonosov Moscow State University. 2021.
Carlson B.A. Communication Systems. McGraw Hill Kogakusha, Ltd., 1968.
Brillouin L. Science and information theory. N.Y.: Academic Press, 1956.
Feigenbaum M.J. Universality in complex discrete dynamics. Los Alamos Theoretical Division Annual Report 1975-1976. 1976.
Barzel B. Barabasi A.-L. Universality in network dynamics. Nature Physics. 2013. Vol. 9. Pp. 673-768,
Gerck E., d Oliveira A.B. Matrix-Variational Method: An efficient approach to bound state eigenproblems. Report number: EAV-12/78. Laboratorio de Estudos Avancados, IAE, CTA. Brazil: S.J. Campos, SP, 1978. Copy online at https://www.researchgate.net/publication/286625459/
Gallas J.A.C., Gerck E., O Connell R.F. Scaling laws for Rydberg atoms in magnetic fields. 1983.
Gerck E., d Oliveira A.B. The non-relativistic three-body problem with potential of the form K1rn K2/r C. Report number: EAV-11/78. Laboratorio de Estudos Avancados, IAE, CTA. Brazil: S.J. Campos, SP, 1978. Copy online at https://www.researchgate.net/publication/286640675/
Gerck E., d Oliveira A.B. Continued fraction calculation of the eigen-values of tridiagonal matrices arising from the Schr dinger equation. Journal of Computational and Applied Mathematics. 1980. No. 6 (1). Pp. 81-82. Copy online at https://www.researchgate.net/publication/242978992/
Gerck E., Gallas J.A.C., d Oliveira A.B. Solution of the Schr dinger equation for bound states in closed form. Physical Review. 1982. No. A 26. P. 1 (1).
Gerck E., d Oliveira A.B., Gallas J.A.C. New approach to calculate bound state eigenvalues. Revista Brasileira de Ensino de Fisica. 1983. No. 13 (1). Pp. 183-300.
Ozhigov Y.I. Constructive physics (physics research and technology). Ed. UK: Nova Science Pub. Inc, 2011. ISBN 1612095534.
Wilson K.G. The renormalization group: Critical phenomena and the Kondo problem. J. Physique Lett. 1975. No. 43. Pp. 211-216,
Gerck E. The exponential difference. Private communication, cited in report number: EAV-12/78. Laboratorio de Estudos Avancados, IAE, CTA, Brazil: S.J. Campos, SP, 1978. Copy online at https://www.researchgate.net/publication/286625459/
Gerck E., Miranda L. Quantum well lasers tunable by long wavelength radiation. Applied Physics Letters. 1984. No. 44 (9). Pp. 837-839.
Ahlfors L. Complex analysis. McGraw-Hill, Inc., 1979.
Havil J. The irrationals. Princeton University Press, 2012.
Khrennikov A.Y. Universality in network dynamics. Springer Science Business Media. 2013. Vol. 427.
Keywords:
tri-state+, bound states, qubit, qutrit, qudit, tri-state+, information, algebraic, quantum, classical, coherence.
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