Mathematical surprises and Dirac's formalism in quantum mechanics
Résumé
Different formalisms are used in quantum mechanics for the description of states and observables: wave mechanics, matrix mechanics and the invariant formalism. We discuss the problems and shortcomings of the invariant formalism as well as those of the bra and ket notation introduced by Dirac in this context. We indicate how all problems can be solved or at least avoided. A series of examples illustrates the raised problems and shows how lack of mathematical concern can readily lead to surprising mathematical contradictions.
