1) Let (0) and (0) be arbitrary functions of the angle 0 which have the property...

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1) Let (0) and (0) be arbitrary functions of the angle 0 which have the property (0) = (0+2) and (0) = (0+2), since the angles 0 and 0 + 2 are physically identical. Show that the operator = - i (0/0) is Hermitian if 0 spans the angular range from 0 to 2 radians. Hint: Calculate the integral integraldisplay 0 d0 6* (0) (0) by parts to show that integraldisplay d 0 * (0) (0) = integraldisplay 0 de [6(0)]*(0). 1) Let (0) and (0) be arbitrary functions of the angle 0 which have the property (0) = (0+2) and (0) = (0+2), since the angles 0 and 0 + 2 are physically identical. Show that the operator = - i (0/0) is Hermitian if 0 spans the angular range from 0 to 2 radians. Hint: Calculate the integral integraldisplay 0 d0 6* (0) (0) by parts to show that integraldisplay d 0 * (0) (0) = integraldisplay 0 de [6(0)]*(0).