  This article mainly consists in the quantum mechanical study of an
adiabatically compressed particle, in an infinitely high well, which we
conjecture, can be considered as the basis of an ideal gas. Thus we prove that,
all the compression energy is, as may be expected, transformed into extra
kinetic energy of the particle. This result frames a quantum mechanical
definition of an ideal gas. It further helps the elucidation of a paradox.
