Editing Unbounded operator (section)

==Importance of self-adjoint operators==
The class of '''self-adjoint operators''' is especially important in mathematical physics. Every self-adjoint operator is densely defined, closed and symmetric. The converse holds for bounded operators but fails in general. Self-adjointness is substantially more restricting than these three properties. The famous [[Self-adjoint operator#Spectral theorem|spectral theorem]] holds for self-adjoint operators. In combination with [[Stone's theorem on one-parameter unitary groups]] it shows that self-adjoint operators are precisely the infinitesimal generators of strongly continuous one-parameter unitary groups, see {{slink|Self-adjoint operator#Self-adjoint extensions in quantum mechanics}}. Such unitary groups are especially important for describing [[time evolution]] in classical and quantum mechanics.