Exceptional point in a simple textbook example

@article{Fernandez2018ExceptionalPI,
  title={Exceptional point in a simple textbook example},
  author={Francisco M. Fern'andez},
  journal={European Journal of Physics},
  year={2018},
  volume={39},
  pages={045005}
}
  • F. Fern'andez
  • Published 24 September 2017
  • Mathematics
  • European Journal of Physics
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 second-order differential equation with constant coefficients. The second one is the well-known 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… 

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