# 顫動

Krekora等人的研究成果[1]，基於二次量子化量子理論（適合描述多粒子量子動力學的理論）顯示出：「量子場論禁止一顆電子顫動現象的出現。」Krekora等人亦將他們量子場論的數值模擬用在描述另一個具有爭議性（且某種程度相關）的現象，稱作克萊因悖論

## 導引

${\displaystyle H\psi (\mathbf {x} ,t)=i\hbar {\frac {\partial \psi }{\partial t}}(\mathbf {x} ,t)\,\!}$

${\displaystyle H=\left(\alpha _{0}mc^{2}+\sum _{j=1}^{3}\alpha _{j}p_{j}\,c\right)\,\!}$

${\displaystyle -i\hbar {\frac {\partial Q}{\partial t}}(t)=\left[H,Q\right]\,\!\;}$

${\displaystyle \hbar {\frac {\partial x_{k}}{\partial t}}(t)=i\left[H,x_{k}\right]=\alpha _{k}\,\!\;.}$

${\displaystyle \hbar {\frac {\partial \alpha _{k}}{\partial t}}(t)=i\left[H,\alpha _{k}\right]=2ip_{k}-2i\alpha _{k}H\,\!\;.}$

${\displaystyle x_{k}(t)=x_{k}(0)+c^{2}p_{k}H^{-1}t+{1 \over 2}i\hbar cH^{-1}(\alpha _{k}(0)-cp_{k}H^{-1})(e^{-2iHt/\hbar }-1)\,\!}$

## 參考文獻

• 原始論文：E. Schrödinger, Über die kräftefreie Bewegung in der relativistischen Quantenmechanik ("On the free movement in relativistic quantum mechanics"), Berliner Ber., pp. 418-428 (1930); Zur Quantendynamik des Elektrons, Berliner Ber, pp. 63-72 (1931)
• A. Messiah, Quantum Mechanics Volume II, Chapter XX, Section 37, pp. 950-952 (1962)