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This exposition is devoted to a consistent treatment of
quantization problems, based on appealing to some nontrivial items
of functional analysis concerning the theory of linear operators in
Hilbert spaces. The authors begin by considering quantization
problems in general, emphasizing the nontriviality of consistent
operator construction by presenting paradoxes to the naive
treatment. It then builds the necessary mathematical background
following it by the theory of self-adjoint extensions. By
considering several problems such as the one-dimensional Calogero
problem, the Aharonov-Bohm problem, the problem of delta-like
potentials and relativistic Coulomb problemIt then shows how
quantization problems associated with correct definition of
observables can be treated consistently for comparatively simple
quantum-mechanical systems. In the end, related problems in quantum
field theory are briefly introduced. This well-organized text is
most suitable for students and post graduates interested in
deepening their understanding of mathematical problems in quantum
mechanics. However, scientists in mathematical and theoretical
physics and mathematicians will also find it useful.
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