X2 1650

the solution to which, subject to the boundary condition x = 0 when £ = 0, is x=v/e. (6.51)

Figure 6.2 shows the results of using a random number generator to compute N values of £ and the corresponding values of x in 100 bins. The computed probability density is shown as dots. As N increases, the dots lie more closely to the exact probability distribution. If for fixed N the same set of calculations is done again and again the distribution of dots will not be exactly the same. This is shown in Fig. 6.3 for 100 bins and two sets of 106 random numbers.

The previous paragraphs are general. Now we have to get specific in order to develop a computational method in detail. For this we need probability distributions for path lengths and scattering directions, which we turn to next.

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