  We determine the exact quantum particle reflection amplitudes for all known
vacua of a_n^(1) affine Toda theories on the half-line with integrable boundary
conditions. (Real non-singular vacuum solutions are known for about half of all
the classically integrable boundary conditions.) To be able to do this we use
the fact that the particles can be identified with the analytically continued
breather solutions, and that the real vacuum solutions are obtained by
analytically continuing stationary soliton solutions. We thus obtain the
particle reflection amplitudes from the corresponding breather reflection
amplitudes. These in turn we calculate by bootstrapping from soliton reflection
matrices which we obtained as solutions of the boundary Yang-Baxter equation
(reflection equation).
  We study the pole structure of the particle reflection amplitudes and uncover
an unexpectedly rich spectrum of excited boundary states, created by particles
binding to the boundary. For a_2^(1) and a_4^(1) Toda theories we calculate the
reflection amplitudes for particle reflection off all these excited boundary
states. We are able to explain all physical strip poles in these reflection
factors either in terms of boundary bound states or a generalisation of the
Coleman-Thun mechanism.

High Energy Physics - Theory;Exactly Solvable and Integrable Systems;Exactly Solvable and Integrable Systems