Name
Abstract | ||
|---|---|---|
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 rho c(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 rho c(t,x,y) is verified by the solution of the complex Fokker-Planck equation. It is shown that quantum probability |psi|2 and classical probability can be integrated under the framework of complex probability rho c(t,x,y), such that they can both be derived from rho c(t,x,y) by different statistical ways of collecting spatial points. |
Year | DOI | Venue |
|---|---|---|
2021 | 10.3390/e23020210 | ENTROPY |
Keywords | DocType | Volume |
complex stochastic differential equation, complex Fokker-Planck equation, quantum trajectory, complex probability, optimal quantum guidance law | Journal | 23 |
Issue | ISSN | Citations |
2 | 1099-4300 | 0 |
PageRank | References | Authors |
0.34 | 0 | 2 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| cianndong yang | 1 | 5 | 1.84 |
| Shiang-Yi Han | 2 | 0 | 0.34 |