细杆屈曲不稳定性的量子特征
The quantum character of buckling instabilities in thin rods
摘要：
在这里，由于轴向体力不可伸展杆的屈曲映射到一维，非相对论，时间无关的量子力学。专注于教学的情况下，杆局限于2D，三个简单的和物理上可实现的应用程序的映射的细节;量子对应的这些是粒子在一个盒子里，粒子在一个三角形函数井，和粒子在一个三角形井。第四个应用程序检查屈曲对应的量子多体问题（在哈特里近似）。通过第五个应用程序，以练习的形式给出，读者可以探索在杆屈曲问题中添加第二个横向尺寸和施加周期性边界条件的令人惊讶的后果。
英文摘要：
Here the buckling of inextensible rods due to axial body forces is mapped to 1d, nonrelativistic, time-independent quantum mechanics. Focusing on the pedagogical case of rods confined to 2d, three simple and physically realizable applications of the mapping are given in detail; the quantum counterparts of these are particle in a box, particle in a delta-function well, and particle in a triangular well. A fourth application examines the buckling counterpart of a quantum many-body problem (in the Hartree approximation). Through a fifth application, given in the form of an exercise, the reader can explore the surprising consequences of adding a second transverse dimension to the rod buckling problem and imposing periodic boundary conditions.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
