Constructing quantum observables and self-adjoint extensions of symmetric operators. II. Differential operators

Autor:	D. M. Gitman, B.L. Voronov, I. V. Tyutin
Rok vydání:	2007
Předmět:	Unbounded operator Algebra Constant coefficients Microlocal analysis General Physics and Astronomy Spectral theorem Extensions of symmetric operators Operator theory Operator norm Fourier integral operator Mathematics
Zdroj:	Russian Physics Journal. 50:853-884
ISSN:	1573-9228 1064-8887
Popis:	We discuss a problem of constructing self-adjoint ordinary differential operators starting from self-adjoint differential expressions based on the general theory of self-adjoint extensions of symmetric operators outlined in [1]. We describe one of the possible ways of constructing in terms of the closure of an initial symmetric operator associated with a given differential expression and deficient spaces. Particular attention is focused on the features peculiar to differential operators, among them on the notion of natural domain and the representation of asymmetry forms generated by adjoint operators in terms of boundary forms. Main assertions are illustrated in detail by simple examples of quantum-mechanical operators like the momentum or Hamiltonian.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::81d46dbd871c23e70423b4e133a73a1a https://doi.org/10.1007/s11182-007-0128-y Zobrazit plný text záznamu Plný text ve formátu PDF