Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Mathematical surprises and Dirac's formalism in quantum mechanics   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 Dirac's abstract Hilbert space
formulation, we devote the second part of our paper to the latter approach: we
discuss the problems and shortcomings of this formalism as well as those of the
bra and ket notation introduced by Dirac in this context. In conclusion, we
indicate how all of these problems can be solved or at least avoided.

35
The categories of this paper are: mtrl-th
11
The categories of this paper are: hep-lat
25
The categories of this paper are: patt-sol
15
The categories of this paper are: nucl-ex
19
The categories of this paper are: eess
34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
6
The categories of this paper are: astro-ph
32
The categories of this paper are: atom-ph
21
The categories of this paper are: adap-org
28
The categories of this paper are: alg-geom
29
The categories of this paper are: funct-an
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
23
The categories of this paper are: solv-int
10
The categories of this paper are: q-bio