1. How are t and r changed when a barrier is translated through d, as in the previous exercise, and has this any observable consequences?

2. As we build the T-matrices for complicated barriers out of those for simple components, it is important that the product of two T -matrices is itself a T-matrix and has the properties that we have just derived. Show that this is so. (This is one of the properties of a mathematical group, and T-matrices provide a representation of the group SU(1, 1).)