= cos 2niY + (Jl+A~ 1 ) sin 21~7 and M2 = cos 26 + T2 sin 21~7 = cos 27~5 + (J~+AJ~) sin 26. Writing the transfer matrix from location 1 to location 2 as Ml2 (there is no need for a bar on top because there is no bump between locations 1 and 2) the relation E, = M12M1M i we get AJ2 -1 = M12AJ1M12 -5- TM-313-A 0402 which shows that the determinant of AJ is invariant within a bump-free region. We can, thus, write U = -IAJI = (Ao1)2 - (AB)iAy) = invariant. Substituting Ay = ~+(cx+A~)~ _ 1+02 B+A:Es - B = we get directly the expression (5A). I am grateful to Dr. for pointing out the error in TM

and to Dr for the derivation of the exact expression of the invariant U, and to both of them for several illuminating discussions