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Self-adjoint Extensions in Quantum Mechanics: General Theory and Applications to Schrödinger and Dirac Equations with Singular Potentials (Progress in ... 62) (Progress in Mathematical Physics, 62) by D.M. Gitman, I.V. Tyutin, B.L. Voronov (auth.) is a nonfiction available to read on EtoBox.
What is Self-adjoint Extensions in Quantum Mechanics: General Theory and Applications to Schrödinger and Dirac Equations with Singular Potentials (Progress in ... 62) (Progress in Mathematical Physics, 62) about?
Quantization of physical systems requires a correct definition of quantum-mechanical observables, such as the Hamiltonian, momentum, etc., as self-adjoint operators in appropriate Hilbert spaces and their spectral analysis. Though a “naïve” treatment exists for dealing with such problems, it is based on finite-dimensional algebra or even infinite-dimensional algebra with bounded operators, resulting in paradoxes and inaccuracies. A proper treatment of these problems requires invoking certain nontrivial notions and theorems from functional analysis concerning the theory of unbounded self-adjoint operators and the theory of self-adjoint extensions of symmetric operators. __Self-adjoint Extensions in Quantum Mechanics__ begins by considering quantization problems in general, emphasizing the nontriviality of consistent operator construction by presenting paradoxes of the naïve treatment. The necessary mathematical background is then built by developing the theory of self-adjoint extensions. Through examination of various quantum-mechanical systems, the authors show how quantization problems associated with the correct definition of observables and their spectral analysis can be treated
Who reads Self-adjoint Extensions in Quantum Mechanics: General Theory and Applications to Schrödinger and Dirac Equations with Singular Potentials (Progress in ... 62) (Progress in Mathematical Physics, 62)?
It is typically read by self-directed learners exploring a subject in depth.
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- Author
- D.M. Gitman, I.V. Tyutin, B.L. Voronov (auth.)
- Publisher
- Birkhäuser Boston
- Published
- 2012
- Language
- EN
- ISBN
- 9781280802577
- Category
- nonfiction
- Subjects
- Mathematics, Science, Physics
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