Matrix Exponential: The time evolution operator is given by the matrix exponential: U ( t ) = e i H t U(t)=e iHt For a matrix A A such that A 2 = I A 2 =I, the exponential can be expressed as: e A t = cos ( t ) I + sin ( t ) A e At =cos( t)I+ sin( t) A In our case, = B 2 =B 2 , so: e i H t = cos ( B t ) I i sin ( B t ) B H e iHt =cos(Bt)I B isin(Bt) H