Applied Mathematics and Mechanics (English Edition) ›› 2017, Vol. 38 ›› Issue (1): 39-56.doi: https://doi.org/10.1007/s10483-017-2151-6

Heng XIAO

- Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China

Heng XIAO

- Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China

**摘要： **

It is reported that there exist deformable media which display quantum effects just as quantum entities do. As such, each quantum entity usually treated as a point particle may be represented by a deformable medium, the dynamic behavior of which is prescribed by four dynamic state variables, including mass density, velocity, internal pressure, and intrinsic angular momentum. In conjunction with the finding of the characteristic equation characterizing the physical nature of such media, it is found that a complex field quantity may be introduced to uncover a perhaps unexpected correlation, i.e., the governing dynamic equations for such media may be exactly reduced to the Schrödinger equation, from which the closed-form solutions for all the four dynamic state variables can be obtained. It turns out that this complex field quantity is just the wavefunction in the Schrödinger equation. Moreover, the dynamic effects peculiar to spin are derivable as direct consequences. It appears that these results provide a missing link in quantum theory, in the sense of disclosing the physical origin and nature of both the wavefunction and the wave equation. Now, the inherent indeterminacy in quantum theory may be rendered irrelevant. The consequences are explained for certain long-standing fundamental issues.

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