Most of the physical laws associated with quantum mechanics are formulated in a math ematical framework where observables are represented as self-adjoint operators in Hilbert
space. These self-adjoint operators are unbounded and therefore very hard to work with.
Stone’s theorem makes it a little bit easier by establishing a bijection between a strongly
continuous one-parameter group and self-adjoint operators.
We began with the needed terminology, and then proved the stones theorem. In addition,
we have indicated some applications of Stone’s theorem , particularly those associated with
quantum mechanics (dilation and rotation in the Cartesian coordinates)