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Nonlinear quantum dynamics in diatomic molecules: Vibration, rotation and spin

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  • Yang, Ciann-Dong
  • Weng, Hung-Jen

Abstract

For a given molecular wavefunction Ψ, the probability density function Ψ∗Ψ is not the only information that can be extracted from Ψ. We point out in this paper that nonlinear quantum dynamics of a diatomic molecule, completely consistent with the probability prediction of quantum mechanics, does exist and can be derived from the quantum Hamilton equations of motion determined by Ψ. It can be said that the probability density function Ψ∗Ψ is an external representation of the quantum state Ψ, while the related Hamilton dynamics is an internal representation of Ψ, which reveals the internal mechanism underlying the externally observed random events. The proposed internal representation of Ψ establishes a bridge between nonlinear dynamics and quantum mechanics, which allows the methods and tools already developed by the former to be applied to the latter. Based on the quantum Hamilton equations of motion derived from Ψ, vibration, rotation and spin motions of a diatomic molecule and the interactions between them can be analyzed simultaneously. The resulting dynamic analysis of molecular motion is compared with the conventional probability analysis and the consistency between them is demonstrated.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:45:y:2012:i:4:p:402-415
    DOI: 10.1016/j.chaos.2012.01.006
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    References listed on IDEAS

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    1. Yang, Ciann-Dong, 2008. "Complex dynamics in diatomic molecules. Part I: Fine structure of internuclear potential," Chaos, Solitons & Fractals, Elsevier, vol. 37(4), pages 962-976.
    2. 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.
    3. Yang, Ciann-Dong, 2007. "Complex tunneling dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 32(2), pages 312-345.
    4. Yang, Ciann-Dong, 2009. "A new hydrodynamic formulation of complex-valued quantum mechanics," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 453-468.
    5. Yang, Ciann-Dong, 2009. "Stability and quantization of complex-valued nonlinear quantum systems," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 711-723.
    6. Yang, Ciann-Dong & Weng, Hung- Jen, 2008. "Complex dynamics in diatomic molecules. Part II: Quantum trajectories," Chaos, Solitons & Fractals, Elsevier, vol. 38(1), pages 16-35.
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