Problem

••• One can define the collision time τ in the following way: The probability P that an el...

••• One can define the collision time τ in the following way: The probability P that an electron suffers a collision during an infinitesimal time interval dt is

P(collision in time dt)= dt/τ (13.35)

Note that the probability that the electron suffers no collision during a time interval dt is then given by

P(no collision in dt) = 1 −dt/τ (13.36)

Consider now the probability P′(t) that a given electron undergoes no collision during a finite time interval t. (a) Show that P′ obeys the equation

[Hint: First, argue that P′(t + dt) = P′(t) (1− dt/τ)(b) Using (13.37), solve for P′(t) and sketch this function. (c) Suppose that a collision occurs at time t − 0. Argue that the probability p″(t) dt that the next collision occurs between time t and t + dt is given by