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| 論文名稱 | Extending quantum probability from real axis to complex plane |
| 發表日期 | 2021-02-08 |
| 論文收錄分類 | SCI |
| 所有作者 | C.D.Yang; S.Y. Han |
| 作者順序 | 第二作者 |
| 通訊作者 | 是 |
| 刊物名稱 | Entropy |
| 發表卷數 | |
| 是否具有審稿制度 | 是 |
| 發表期數 | |
| 期刊或學報出版地國別/地區 | NATSWE-瑞典王國 |
| 發表年份 | 2021 |
| 發表月份 | 2 |
| 發表形式 | 電子期刊 |
| 所屬計劃案 | 無 |
| 可公開文檔 |
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| 可公開文檔 |
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| 可公開文檔 |
[英文摘要] :
Probability is an important question in the ontological interpretation of quantum mechanics. It has been discussed in some trajectory interpretations such as Bohmian mechanics and stochastic mechanics. New questions arise when the probability domain extends to the complex space, including the generation of complex trajectory, the definition of the complex probability, and the relation of the complex probability to the quantum probability. The complex treatment proposed in this article applies the optimal quantum guidance law to derive the stochastic differential equation governing a particle’s random motion in the complex plane. The probability distribution ρc(t,x,y) of the particle’s position over the complex plane z=x+iy is formed by an ensemble of the complex quantum random trajectories, which are solved from the complex stochastic differential equation. Meanwhile, the probability distribution ρc(t,x,y) is verified by the solution of the complex Fokker–Planck equation. It is shown that quantum probability |Ψ|2 and classical probability can be integrated under the framework of complex probability ρc(t,x,y), such that they can both be derived from ρc(t,x,y) by different statistical ways of collecting spatial points.
