I want to "show that the classical probability density describing a particle in an infinite square well of dimension L is P(x) = 1/L." I know that classically, the particle bounces back and forth with constant kinetic energy and at constant speed, so at any given time it is equally likely to be found at any location in the well. It seems intuitively obvious that the probability that the particle will be between 0 and .25L, for example, at any particular moment, would be 1/4. Between .25L and .75L the probability must be 1/2. But how do I show formally that the probability density function is 1/L?