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Constructing quantum observables and self-adjoint extensions of symmetric operators. I.
- Source :
- Russian Physics Journal; Jan2007, Vol. 50 Issue 1, p1-31, 31p
- Publication Year :
- 2007
-
Abstract
- Constructing physical observables as self-adjoint operators under quantum-mechanical description of systems with boundaries and/or singular potentials is a nontrivial problem. We present a comparative review of various methods for constructing ordinary self-adjoint differential operators associated with self-adjoint differential expressions based on the general theory of self-adjoint extensions of symmetric operators. The exposition is nontraditional and is based on the concept of asymmetry forms generated by adjoint operators. The main attention is given to a specification of self-adjoint extensions by self-adjoint boundary conditions. All the methods are illustrated by examples of quantum-mechanical observables like momentum and Hamiltonian. In addition to the conventional methods, we propose a possible alternative way of specifying self-adjoint differential operators by explicit self-adjoint boundary conditions that generally have an asymptotic form for singular boundaries. A comparative advantage of the method is that it allows avoiding an evaluation of deficient subspaces and deficiency indices. The effectiveness of the method is illustrated by a number of examples of quantum-mechanical observables. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 10648887
- Volume :
- 50
- Issue :
- 1
- Database :
- Complementary Index
- Journal :
- Russian Physics Journal
- Publication Type :
- Academic Journal
- Accession number :
- 25335580
- Full Text :
- https://doi.org/10.1007/s11182-007-0001-z