Forster, Malcolm R. and Krioukov, Alexei (2002) How to �See Through� the Ideal Gas Law in Terms of the Concepts of Quantum Mechanics. [Preprint]

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Abstract

Textbooks in quantum mechanics frequently claim that quantum mechanics explains the success of classical mechanics because �the mean values [of quantum mechanical observables] follow the classical equations of motion to a good approximation,� while �the dimensions of the wave packet be small with respect to the characteristic dimensions of the problem.� The equations in question are Ehrenfest�s famous equations. We examine this case for the one-dimensional motion of a particle in a box, and extend the idea deriving a special case of the ideal gas law in terms of the mean value of a generalized force, which has been used in statistical mechanics to define �pressure�. The example may be an important test case for recent philosophical theories about the relationship between micro-theories and macro-theories in science.

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