Question

(a) If A is Hermitian, show that e^iA is unitary 

(b) What operator may be used to distinguish between 

(a) e^ikx and e^−ikx (b) sinax and cosax? 

Answer 1

(a) Let f = e^{i A} ; then f ^† = ( e^{i A})^† = e^{−i A} 

Therefore f^† f = e^{−i A}e^{i A} = 1 

Thus e^{i A} is unitary. (b) (a) Momentum (b) Parity