Consider an unbound particle of mass m with a binary internal degree of freedom propagating with energy E in one space dimension under the influence of the potential where Vo > 0. V₁ -{*G² ). V(x) = #> 0 HAO (a) For each region, r < 0 and r> 0, find a complete set of independent energy eigenfunctions in terms of m, Vo, E, and any physical and mathematical constants. (Boundary conditions can be ignored for this part.) (b) Suppose that the particle is prepared as a state initially propagating in the +x direction from - with the internal degree of freedom in the state correspond- ing to (1). Find the probability, in terms of m, Vo, E, and any physical and mathematical constants, that the particle is reflected from x = O with the internal degree of freedom in the state corresponding to (9).