Show that if H is a hermitian operator, then U = eiH is unitary.
UU† = I for a unitary matrix
A†=A for hermitian operator
I = identity matrix
The Attempt at a Solution
Here is what I have. U = eiH multiplying both by U† gives UU† = eiHU† then replacing U† with U-1 (a property of unitary matrices) I have UU† = eiHU-1 and so UU† = eiHe-iH = ei(H-H)=e0 = 1 = I. I don't think this is right though...