论文标题
细杆中屈曲不稳定性的量子特征
The quantum character of buckling instabilities in thin rods
论文作者
论文摘要
在这里，由于轴向体力引起的不可延迟杆的屈曲映射到1D，非依赖性，时间无关的量子力学。详细给出了限制于2D的杆的教学案例，详细给出了三个简单且物理上可实现的应用；它们的量子对应物是一个盒子中的粒子，粒子在三角孔中，三角形井中的粒子。第四个应用程序检查了量子多体问题的屈曲对应物（在哈特里近似中）。通过以练习形式给出的第五个应用程序，读者可以探索在杆屈曲问题中增加第二个横向维度并施加周期性边界条件的令人惊讶的后果。
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.
