In 1-D let T

_{L} be an operator defined on the position eigenstates |x> such that T

_{L}|x>=|x+L>.

Find the matrix elements T

_{L}(x,x

^{'})=<x

^{'}|T

_{L}|x> and construct an explicit expansion for this operator in the position representation. Show that “in the position representation”

, i.e. T

_{L }shifts the state of the system along the positive x axis. Is T

_{L }diagonal in the position representation?

I have T

_{L}(x,x

^{'})=

Here is where I really get confused. Should the delta be reversed? Could someone please help me understand this better?

Thanks