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Statistical Physics. Including Applications to Condensed Matter
A course of Quantum Mechanics, like the one taught at Ecole Polytechnique,
is devoted to the description of the state of an individual particle, or possibly
of a few ones. Conversely, the topic of this book will be the study of systems∗
containing very many particles, of the order of the Avogadro number N, for
example the molecules in a gas, the components of a chemical reaction, the
adsorption sites for a gas on a surface, the electrons of a solid. You certainly
previously studied this type of system, using Thermodynamics which is ruled
by “exact” laws, such as the ideal gas one. Its physical parameters, that can be
measured in experiments, are macroscopic quantities like its pressure, volume,
temperature, magnetization, etc.
It is now well-known that the correct microscopic description of the state of
a system, or of its evolution, requires the Quantum Mechanics approach and
the solution of the Schroedinger equation, but how can this equation be solved
when such a huge number of particles comes into play ? Printing on a listing
the positions and velocities of the N molecules of a gas would take a time
much longer that the one elapsed since the Big Bang ! A statistical description
is the only issue, which is the more justified as the studied system is larger,
since the relative fluctuations are then very small (Ch. 1).
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