Exceptional point in a simple textbook example
Abstract
We propose to introduce the concept of exceptional points in intermediate courses on mathematics and classical mechanics by means of simple textbook examples. The first one is an ordinary secondorder differential equation with constant coefficients. The second one is the wellknown damped harmonic oscillator. From a strict mathematical viewpoint both are the same problem that enables one to connect the occurrence of linearly dependent exponential solutions with a defective matrix which cannot be diagonalized but can be transformed into a Jordan canonical form.
 Publication:

European Journal of Physics
 Pub Date:
 July 2018
 DOI:
 10.1088/13616404/aab6df
 arXiv:
 arXiv:1710.00067
 Bibcode:
 2018EJPh...39d5005F
 Keywords:

 Physics  Classical Physics
 EPrint:
 doi:10.1088/13616404/aab6df