Symmetric random walk on a regular lattice with an elastic barrier: diffusion equation and the boundary condition

We examine here the symmetric random-walk model in which a particle can jump only to adjacent sites on a regular lattice, and discuss, in the light of the works of Chandrasekhar, Goodrich, van Kampen, and Oppenheim, the reduction of the problem of random walk in the presence of an elastic barner to a boundary value problem.