薛定谔方程、零点电磁辐射和光电效应
The Schrödinger equation, the zero-point electromagnetic radiation and the photoelectric effect
摘要：
数学概率振幅的薛定谔方程是从广义相空间刘维尔方程导出的，该方程适用于质量为M的微观粒子在势V（x）中的运动。粒子相空间概率密度记为W（x，p，t），整个系统沉浸在“真空”零点电磁辐射中。我们表明，广义刘维尔方程减少到一个非量子化的刘维尔方程在平衡极限，小的辐射修正相互抵消近似。我们的推导将基于非量化相空间概率分布W（x，p，t）的简单傅立叶变换。为了方便起见，我们在这个傅里叶变换中引入一个辅助常数α，具有作用维数，以及一个由y表示的辅助坐标。我们将证明α等于存在于薛定谔方程动量算符中的普朗克常数。此外，我们将证明这个动量算符与无处不在的零点电磁辐射密切相关。同样重要的是，我们没有假设数学振幅ψ（x，t）是德布罗意物质波，换句话说，我们的工作中没有使用波粒二象性假设。我们的研究的标准解释的光电效应的影响进行了讨论，考虑的主要特征的现象。我们还简要地提到了零点辐射在隧道效应和康普顿效应中的作用。
英文摘要：
A Schrödinger type equation for a mathematical probability amplitude ψ(x,t), is derived from the generalized phase space Liouville equation valid for the motion of a microscopic particle, with mass M, moving in a potential V(x). The particle phase space probability density is denoted W(x,p,t) and the entire system is immersed in the "vacuum" zero-point electromagnetic radiation . We show that the generalized Liouville equation is reduced to a non-quantized Liouville equation in the equilibrium limit where the small radiative corrections cancel each other approximately. Our derivation will be based on a simple Fourier transform of the non-quantized phase space probability distribution W(x,p,t). For convenience, we introduce in this Fourier transform an auxiliary constant α, with dimension of action, and an auxiliary coordinate denoted by y. We shall prove that α is equal to the Planck's constant present in the momentum operator of the Schrödinger equation. Moreover, we shall show that this momentum operator is deeply related with the ubiquitous zero-point electromagnetic radiation. It is also important to say that we do not assume that the mathematical amplitude ψ(x,t) is a de Broglie matter-wave, in other words, the wave-particle duality hypothesis is not used within our work. The implications of our study for the standard interpretation of the photoelectric effect is discussed by considering the main characteristics of the phenomenon. We also mention, briefly, the effects of the zero-point radiation in the tunnelling phenomenon and in the Compton's effect.
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