Synthesizing quantum probability by a single chaotic complex-valued trajectory

Ciann Dong Yang, Chia Hung Wei

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)


The current trajectory interpretation of quantum mechanics is based on an ensemble viewpoint that the evolution of an ensemble of Bohmian trajectories guided by the same wavefunction Ψ converges asymptotically to the quantum probability |Ψ|2. Instead of the Bohm's ensemble-trajectory interpretation, the present paper gives a single-trajectory interpretation of quantum mechanics by showing that the distribution of a single chaotic complex-valued trajectory is enough to synthesize the quantum probability. A chaotic complex-valued trajectory manifests both space-filling (ergodic) and ensemble features. The space-filling feature endows a chaotic trajectory with an invariant statistical distribution, while the ensemble feature enables a complex-valued trajectory to envelop the motion of an ensemble of real trajectories. The comparison between complex-valued and real-valued Bohmian trajectories shows that without the participation of its imaginary part, a single real-valued trajectory loses the ensemble information contained in the wavefunction Ψ, and this explains the reason why we have to employ an ensemble of real-valued Bohmian trajectories to recover the quantum probability |Ψ|2.

Original languageEnglish
Pages (from-to)428-437
Number of pages10
JournalInternational Journal of Quantum Chemistry
Issue number6
Publication statusPublished - 2016 Mar 15

All Science Journal Classification (ASJC) codes

  • Atomic and Molecular Physics, and Optics
  • Condensed Matter Physics
  • Physical and Theoretical Chemistry


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