Very simple question: Why doesn't Mathematica simplify this square root expression?
Refine[Sqrt[Exp[I p]], p > 0] // FullSimplify
It should give
Where is my mistake?
Just avoid the branch cut:
Refine[Sqrt[Exp[I p]], π > p > 0] (* ==> E^((I p)/2) *)
The branch cut of the square-root function doesn't allow Mathematica to simplify the expression without the restriction on
p from above.
See also the related question and answer here: Using Solve to solve the equation x1/3=−1