The quantum character of buckling instabilities in thin rods

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 counterpa...

Full description

Saved in:
Bibliographic Details
Published in:American journal of physics 2020-10, Vol.88 (10), p.845-850
Main Author: Engstrom, T. A.
Format: Article
Language:English
Subjects:
Boundary conditions
Buckling
Particle size
Quantum dots
Quantum physics
Quantum theory
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:0002-9505
1943-2909
DOI:10.1119/10.0001684