标题： 超对称量子力学中能级 crossing 的半经典方法 显示英文标题

标题： A Semiclassical Approach to Level Crossing in Supersymmetric Quantum Mechanics

摘要： 超对称量子力学（SUSY QM）的技术已被广泛用于研究由超势能$\phi(x)$描述的束缚态问题。在解析延拓$\phi(x) \to i\phi(x)$下，一对超伙伴束缚态问题被转化为连续区中的两态能级穿越问题。物质增强的中微子振荡描述涉及一个能级穿越问题。我们用超对称量子力学的技术来处理这个问题。为了使不熟悉中微子振荡及其描述的读者也能理解本文的其余部分，提供了足够的细节。物理学中有许多其他形式完全相同的能级穿越问题。特别注意的是，不同的半经典技术会产生不同的结果。最好的结果是通过一种明确认识到系统超对称性质的均匀近似方法得到的。 显示英文摘要

摘要： Much use has been made of the techniques of supersymmetric quantum mechanics (SUSY QM) for studying bound-state problems characterized by a superpotential $\phi(x)$. Under the analytic continuation $\phi(x) \to i\phi(x)$, a pair of superpartner bound-state problems is transformed into a two-state level-crossing problem in the continuum. The description of matter-enhanced neutrino flavor oscillations involves a level-crossing problem. We treat this with the techniques of supersymmetric quantum mechanics. For the benefit of those not familiar with neutrino oscillations and their description, enough details are given to make the rest of the paper understandable. Many other level-crossing problems in physics are of exactly the same form. Particular attention is given to the fact that different semiclassical techniques yield different results. The best result is obtained with a uniform approximation that explicitly recognizes the supersymmetric nature of the system.