A _[one-parameter](One-parameter%20groups.md) [unitary](Unitary%20operators.md) group_ is defined as a family of unitary operators, $\mbox{U}(t)$ for $t\in\mathbb{R}$ with the [properties](One-parameter%20groups.md#Properties%20of%20one-parameter%20groups) of a one-parameter group. These operators form a one-parameter unitary group on a [[Hilbert Space]], $\mathcal{H}.$ # Examples * In particular we are often interested in one-parameter unitary groups that are also [strongly continuous](Strong%20continuity.md) since those are the kind of one-parameter unitary subgroups most likely to appear in physical applications of this theory. #MathematicalFoundations/Algebra/AbstractAlgebra/GroupTheory/Lie/LieGroups/Algebras/LieAlgebras #MathematicalFoundations/Algebra/AbstractAlgebra/GroupTheory/Lie/LieGroups