Chp 7 Quantum Statistics

Question 1

Grandpartition function

i.e. gibbs sum

Answer 1

$\mathscr{Z} = \sum_s e^{-[E(s)-\mu N(s)}/kT$

Question 2

P(s)

Answer 2

$\frac{1}{\mathscr{Z}}e^{-[E(s) -\mu N(s)}/kT$

Question 3

Thing to remmeber when summing over states

Answer 3

include N = 0 state so the first term is 1

Question 4

Quantum statistics

Answer 4

Most NB application of Gibbs factors

the study of dense systems in which 2+ identital particles have a reasonable chance of wanting to occupy the same single particle state

Question 5

Which formula breaks down from chap 6 and why

Answer 5

For system of N indistinguishable noninteracting particles
$$Z=\frac{1}{N!}Z_1^N$$
breaks down

This only works if the particles are always in DIFFERENT states.
chp 7 we focus on dense sys where can be in same state

Question 6

Bosons

Answer 6

Particles that CAN share a state with another of the same species
Photons

integer spins (1 2 3, in units of $h/2\pi$)

Question 7

Fermions

Answer 7

Cannot share state with another of same species
Protons neutrons

Due to Pauli Excl princ

Half integer spins (1/2 3/2)

Question 8

When does it not matter if particles are femions or bosons

Answer 8

# available single particle states >> # particles
\$\$Z_1 \ >> \ N\$\$

The average distance vbetween aprticles must be much greater than the avg de Broglie wavelength

Question 9

What does the the condition on particles being bosons or fermions mattering hinge on

Answer 9

Condiiton dep on density of sys
temp
mass of the particels (through $v_Q$)

Question 10

Which kinds of systems vioalte the condition and become liek quantum gases

Answer 10

Very dense (neutron star)
Very cold (liq helium)
Composed of very light paticles (e- is a metal or photons in hot oven)
Phonons (quantised units of vibrational energy in a solid)