真实量子力学中的散射与隧穿
Scattering and Tunneling in Real Quantum Mechanics
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中文总结 AI 辅助
该研究建立真实量子力学的演化方程，推导其演化算子性质，构建对应散射理论，证明其微分散射截面、隧穿概率与标准复量子力学结果一致。
中文摘要 AI 辅助
我们建立了演化方程的一般形式，并研究真实量子力学中的散射与隧穿问题。我们证明了实凯勒空间上斯通定理的类似结论，推导得到对应的一般演化方程，其演化算子兼具正交性与辛性。我们基于实波算子及相关S矩阵构建散射理论；对所考虑的一类势场，我们证明其微分散射截面与标准复量子力学中的结果等价，同时表明真实量子力学中的隧穿概率与复量子力学中的完全相同。
英文摘要
We establish the general form of the evolution equation and study scattering and tunneling in real quantum mechanics. We prove an analogue of Stone's theorem for a real Kahler space and derive the corresponding general evolution equation, whose evolution operator is both orthogonal and symplectic. We formulate scattering theory in terms of real wave operators and the associated S-matrix. For the class of potentials considered, we show that the differential scattering cross section is equivalent to that obtained in standard complex quantum mechanics. We also show that the tunneling probability in real quantum mechanics is identical to that in complex quantum mechanics.
