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T; chemical potential
considering a system in contact with a reservoir that can exchange energy and particles with it, the reservoir now provides constant — and constant — —
grand partition function
the sum over all possible states, including all possible values of N for each state
multiple occupancy of states
the grand partition function allows for —
classical; quantum; wave packets
for an ideal gas, when Z1 » N, it’s in the — regime, and particles do not have to share a — state because their — — hardly ever overlap
low; large
multiple occupancy becomes an issue at — temps because the quantum volume will be —
single definite quantum; thermal equilibrium
considering the distribution for quantum particles at multiple occupancy in state n; the — — — state is the system, and all other states (reservoir) must be in — — with the system
grand partition function
the probability that a particle state of energy ei is occupied by n particles
zero; infinity; partition
if the average energy of a single particle is — or temperature goes to —, then multiplicity is the — function
step function; fermi energy
FD: for T = 0, nFD is a — —, and mu is equal to — —
decreases; increases; higher energy states
FD: as T increases, the occupation below e = mu — while occupation above —; this reflects particles being thermally excited to — — —
defined; does not converge; diverges
BE: for e > mu, nBE is —, otherwise nBE —. At e = mu, nBE —
non-negative
for bosons occupation n can be any — integer
1; 0
for fermions, occupation n can be either — or —
diverges; Bose-Einstein condensation
BE: as mu goes to 0, the occupancy of the ground state — resulting in — —
N
MB: given N independent particles in total, the average distribution of particles at a given energy is — * 1/Ze^-e/kT
greater
for (e - mu)/kT is — than 1, the three distributions are equal
n(e,T)*p(e)
occupancy of energy levels D(e,T) between e and e+de is an integral over
total number of particles N
the integral over the occupancy over all energy levels is the —
e*n(e,T)*p(e)
the thermodynamic (average) energy is calculated as the integral over all energy states of —
real
for — particles, N is fixed and independent of temperature, and mu is dependent on temperature
virtual; helmholtz; 0
for — particles, N is not fixed and is determined by the value which minimizes — free energy, therefore mu is —
degenerate fermi gas
modelled by a non-interacting fermion gas in a box, which can be applied to metals, in which the lattice potential is then approximated by the inf potential well
quantum volume; volume
to determine whether electrons in the free e gas are in the quantum regime at a certain temperature, one must compare the — at that temperature with the — per unit cell
fermi energy
at T=0 for a degenerate ½ spin fermi gas, mu is equal to
fermi energy
quantity determined by highest possible energy levels occupied by a particle
2
when it comes to fermions, to compute N we must take into account — spin states
en²
for a single fermion in a gas, the energy is —
fermi temperature
temp range over which quantum properties (FD statistics) dominate
less
when mu is — than 0, at higher temperatures, classical ideal gas behavior is achieved
0
the transition from a quantum gas to a classical gas occurs at a temperature where mu =
eF/k
fermi temperature is defined as TF =
