科技英語翻譯3
Although all systems in the ensemble are composed of
the same type of particles with the same kind of interactions,
under the same external conditions, the distribution of particles
among the different values of microscopic energies
~microstate! will differ from system to system. Nevertheless,
according to statistical mechanics the majority of the systems
in the ensemble will be in the same equilibrium state ~macrostate!,
which implies that there will be a most probable
distribution of particles, whose parameters will be associated
with the macroscopic state. Even though the interaction is
the same, the form of the distribution will be determined by
whether the mechanical treatment given to the particles is
classical or quantum. The conditions to apply for one or the
other are established through the Heinsenberg uncertainty
principle (2pDqDp>h with h being Planck’s constant!,
which restricts the accuracy with which position, (Dq), and
momentum, (Dp), can be simultaneously ascribed to a particle,
or energy and time of measurement.
A comparison of the number of particles, N, with the
number of energy states, «i , available to them will lead to a
criterion for the use of quantum or classical mechanics.
Thus, if the number of states is very large then the energy
may be regarded as continuous and classical mechanics will
be acceptable. An equivalent approach4 is to compare the
average distance, (V/N)1/3, among particles of mass m, contained
in a volume V and at temperature T, with the associated
de Broglie’s wavelength (A2mkT, k being Boltzmann’s
constant! so that quantum mechanics is required when the
wavelength is larger than the average distance, since momentum
and position are not well determined under this condition.
Quantum mechanically, care should be taken to account
for the so-called Pauli exclusion principle,5 since it will limit
the number of particles in a given state. If the occupation
number is restricted, then the resulting distribution will be
that of Fermi–Dirac; otherwise, the Bose–Einstein distribution
will describe the occupation of the accessible states.6
Both distributions have the Boltzmann distribution as the
asymptotic limit, which results from the classical treatment
of the particles and does not restrict the occupation number.