In the case of radiotherapy, the photons penetrate the body and can interact with the structure of the material, either diverting (Rayleigh scattering) or diverting and generating electrons (Compton scattering, photoelectric effect and pair creation).

This means that the probability of interaction is not a constant factor. On one side there are a number of different mechanisms on the other side these may depend on the properties of the photon (in particular its energy).

In the one-dimensional case we already assumed that the particle reversed its direction of travel each time it interacted. In this case we only had two possible states, that of continuing to propagate and that of being reflected. However it is easy to imagine a situation in which depending on the energy that it has

- loses and remains with a different residual energy

- change or not the direction of propagation

In the multimensional case it is no longer possible to expect an univocal relationship between the initial and the final state. In general they can vary:

- the direction in which the propagation and

- the energy it conserves

The change of direction confront us to the problem of which we can only work with discrete addresses which affects us the traditional function that we wish to assume.

The fact that the resulting state is not unique leads us to have a range of final states and necessity to work with distributions of these. As in the case of the position, it is thus necessary to introduce a discretization of parameters such as energy and the moment/velocity/direction of the particle.

In this way, the probability of transition is no longer simply the probability of an event occurring, it is the probability of an event occurring and a possible outcome.