DISTRIBUTION AND SPECTRUM OF FLUCTUATIONS OF A BROWNIAN PARTICLE IN A POTENTIAL WELL WITH REFLECTING WALLS.

We examine Brownian motion in a square well with reflecting walls. An exact solution is obtained for the corresponding Einstein-Fokker-Planck equation, which is used to find the coordinate correlation function in explicit form. The correlation function, normalized to the square of the distance between the walls, typically exhibits a similarity property: its behavior as a function of time, friction, temperature, and wall separation reduces to a function of one simple combination of those four quantites. The limiting cases of low and high friction are investigated in detail, with explicit expressions being derived for the spectrum.