One-Dimensional Semi-infinite Systems Solutions

In this chapter, we impose a boundary condition (BC) as well as an initial condition to solve the diffusion equation in a semi-infinite system. The BC can be described mathematically by the Dirichlet and Neumann BCs. With Dirichlet BCs, we can define the perfect absorbing boundary, while Neumann BCs are used to describe reflecting and radiation boundaries. As we will see, the properties of the propagator and its flux at the boundary become essential when defining BCs.