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• Self-adjoint_operator abstract "In mathematics, a self-adjoint operator on a complex vector space V with inner product is an operator (a linear map A from V to itself) that is its own adjoint: . If V is finite-dimensional with a given basis, this is equivalent to the condition that the matrix of A is Hermitian, i.e., equal to its conjugate transpose A*. By the finite-dimensional spectral theorem, V has an orthonormal basis such that the matrix of A relative to this basis is a diagonal matrix with entries in the real numbers. In this article, we consider generalizations of this concept to operators on Hilbert spaces of arbitrary dimension.Self-adjoint operators are used in functional analysis and quantum mechanics. In quantum mechanics their importance lies in the Dirac–von Neumann formulation of quantum mechanics, in which physical observables such as position, momentum, angular momentum and spin are represented by self-adjoint operators on a Hilbert space. Of particular significance is the Hamiltonianwhich as an observable corresponds to the total energy of a particle of mass m in a real potential field V. Differential operators are an important class of unbounded operators.The structure of self-adjoint operators on infinite-dimensional Hilbert spaces essentially resembles thefinite-dimensional case, that is to say, operators are self-adjoint if and only if they are unitarily equivalent to real-valued multiplication operators. With suitable modifications, this result can be extended to possibly unbounded operators on infinite-dimensional spaces. Since an everywhere defined self-adjoint operator is necessarily bounded, one needs be more attentive to the domain issue in the unbounded case. This is explained below in more detail.".
• Self-adjoint_operator wikiPageExternalLink book-schroe.
• Self-adjoint_operator wikiPageID "187408".
• Self-adjoint_operator wikiPageRevisionID "602245709".
• Self-adjoint_operator date "November 2013".
• Self-adjoint_operator hasPhotoCollection Self-adjoint_operator.
• Self-adjoint_operator reason "remove Hermitian operators; "H is Hermitian " and "Bounded symmetric operators are also called Hermitian." is contradicting.".
• Self-adjoint_operator subject Category:Hilbert_space.
• Self-adjoint_operator subject Category:Operator_theory.
• Self-adjoint_operator comment "In mathematics, a self-adjoint operator on a complex vector space V with inner product is an operator (a linear map A from V to itself) that is its own adjoint: . If V is finite-dimensional with a given basis, this is equivalent to the condition that the matrix of A is Hermitian, i.e., equal to its conjugate transpose A*. By the finite-dimensional spectral theorem, V has an orthonormal basis such that the matrix of A relative to this basis is a diagonal matrix with entries in the real numbers.".
• Self-adjoint_operator label "Endomorphisme autoadjoint".
• Self-adjoint_operator label "Operador autoadjunto".
• Self-adjoint_operator label "Operatore autoaggiunto".
• Self-adjoint_operator label "Selbstadjungierter Operator".
• Self-adjoint_operator label "Self-adjoint operator".
• Self-adjoint_operator label "エルミート作用素".
• Self-adjoint_operator sameAs Selbstadjungierter_Operator.
• Self-adjoint_operator sameAs Αυτοσυζυγής_τελεστής.
• Self-adjoint_operator sameAs Endomorphisme_autoadjoint.
• Self-adjoint_operator sameAs Operatore_autoaggiunto.
• Self-adjoint_operator sameAs エルミート作用素.
• Self-adjoint_operator sameAs 자기수반작용소.
• Self-adjoint_operator sameAs Operador_autoadjunto.
• Self-adjoint_operator sameAs m.019msh.
• Self-adjoint_operator sameAs Q6500908.
• Self-adjoint_operator sameAs Q6500908.
• Self-adjoint_operator wasDerivedFrom Self-adjoint_operator?oldid=602245709.
• Self-adjoint_operator isPrimaryTopicOf Self-adjoint_operator.