Page 39 - STATISTICAL MECHANICS: From First Principles to Macroscopic Phenomena
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Problems                             25


                 where η is a real positive number and N is a real positive number going to infinity
                                                 b

                 in the thermodynamics limit while E b /N approaches a finite constant. Find β in this
                                                 b
                 case.
            1.3  Find the classical distribution functions for the following one dimensional systems
                 as a function of initial conditions.
                   A particle confined to a box of length a by elastic walls.
                   A one dimensional harmonic oscillator, spring constant K.
                   A ball in the Earth’s gravitational field bouncing elastically from a floor.
                   A pendulum with arbitrary amplitude.
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