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The origin and proof of quantization axiom p→pˆ=-iℏ∇ in complex spacetime

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  • Yang, Ciann-Dong

Abstract

The quantization axiom p→pˆ=-iℏ∇ is the kernel in constructing quantum-mechanical systems; however, it was proposed without proof and even till now no formal proof has been given about its origin and validity by using fundamental theory of mechanics. This paper aims to show that quantum operators have the root in complex spacetime and can be derived naturally from complex-extended Hamilton equations of motion. The derivation of quantum operators from Hamilton mechanics is coordinate-independent and thus allows us to deduce operators directly from any curved spacetime without transforming back to Cartesian space.

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  • Yang, Ciann-Dong, 2007. "The origin and proof of quantization axiom p→pˆ=-iℏ∇ in complex spacetime," Chaos, Solitons & Fractals, Elsevier, vol. 32(2), pages 274-283.
    • Handle: RePEc:eee:chsofr:v:32:y:2007:i:2:p:274-283
    DOI: 10.1016/j.chaos.2006.04.051
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    References listed on IDEAS

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    1. El Naschie, M.S., 2006. "Hilbert, Fock and Cantorian spaces in the quantum two-slit gedanken experiment," Chaos, Solitons & Fractals, Elsevier, vol. 27(1), pages 39-42.
    2. El Naschie, M.S., 2005. "A new solution for the two-slit experiment," Chaos, Solitons & Fractals, Elsevier, vol. 25(5), pages 935-939.
    3. El Naschie, M.S., 2005. "Non-Euclidean spacetime structure and the two-slit experiment," Chaos, Solitons & Fractals, Elsevier, vol. 26(1), pages 1-6.
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    Cited by:

    1. Yang, Ciann-Dong & Wei, Chia-Hung, 2007. "Parameterization of all path integral trajectories," Chaos, Solitons & Fractals, Elsevier, vol. 33(1), pages 118-134.
    2. Yang, Ciann-Dong & Weng, Hung-Jen, 2012. "Nonlinear quantum dynamics in diatomic molecules: Vibration, rotation and spin," Chaos, Solitons & Fractals, Elsevier, vol. 45(4), pages 402-415.
    3. Yang, Ciann-Dong, 2008. "On the existence of complex spacetime in relativistic quantum mechanics," Chaos, Solitons & Fractals, Elsevier, vol. 38(2), pages 316-331.

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