Selfadjoint Extensions In Quantum Mechanics: General Theory And Applications To Schrdinger And Dirac Equations With Singular Po,Used

Selfadjoint Extensions In Quantum Mechanics: General Theory And Applications To Schrdinger And Dirac Equations With Singular Po,Used

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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 selfadjoint extensions. By considering several problems such as the onedimensional Calogero problem, the AharonovBohm problem, the problem of deltalike potentials and relativistic Coulomb problemIt then shows how quantization problems associated with correct definition of observables can be treated consistently for comparatively simple quantummechanical systems. In the end, related problems in quantum field theory are briefly introduced. This wellorganized 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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