求解势阱问题中边界条件的数学推证

求解势阱或势垒的问题是量子力学中一项非常重要的内容,对于边界条件的深刻认识与准确应用是正确求解这类问题的一个重要环节。现行的大部分的量子力学教材并未对边界条件给出完整的推证,仅是在解题的过程中直接给出相应的边界条件或根据物理含义给出文字阐述,本文就针对以上不足从数学的角度推出边界条件并对适用范围进行了简单的讨论。

The Mathematical Reasoning and Discussion of Boundary Conditions Under Solving Potential Well Problems

It's a very important content in quantum mechanics to solve the problems of potential wells or potential hills. The deep acknowledgement and accurate application of the boundary conditions are an important link to the solution of the problems of this kind. But most of the current quantum mechanics textbooks have not provided a complete reasoning to the boundary conditions. They only directly provide the corresponding boundary condition in the solution of a problem or make an explanation in words according to its physics meaning Aiming at the above insufficiency, this article deduces the boundary conditions from the point of mathematics and simply discusses its scope of application.