Mathematical surprises and Dirac's formalism in quantum mechanics

@article{Gieres1999MathematicalSA,
  title={Mathematical surprises and Dirac's formalism in quantum mechanics},
  author={François Gieres},
  journal={Reports on Progress in Physics},
  year={1999},
  volume={63},
  pages={1893-1931}
}
  • F. Gieres
  • Published 22 July 1999
  • Physics
  • Reports on Progress in Physics
By a series of simple examples, we illustrate how the lack of mathematical concern can readily lead to surprising mathematical contradictions in wave mechanics. The basic mathematical notions allowing for a precise formulation of the theory are then summarized and it is shown how they lead to an elucidation and deeper understanding of the aforementioned problems. After stressing the equivalence between wave mechanics and the other formulations of quantum mechanics, i.e. matrix mechanics and… 

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