How to See Through the Ideal Gas Law in Terms of the Concepts of Quantum Mechanics

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Forster, Malcolm R.; Krioukov, Alexei
preprint description
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.