Quantum Statistics

Question 1

What is the exchange operator?

Answer 1

P₁₂ swaps the positions of the particles
r₁–>r₂
r₂–>r ₁

Question 2

What are the types of exchange symmetry?

Answer 2

Symmetric
Anti symmetric

Question 3

What type of particles are symmetric under particle exchange?

Answer 3

Bosons

Question 4

What type of particles are anti symmetric under particle exchange?

Answer 4

Fermions

Question 5

What spin do bosons have?

Answer 5

Integer spin

Question 6

What spin do fermions have?

Answer 6

Half integer spin

Question 7

What is the combined wavefunction?

Answer 7

|Ψ>=|Φ>|Φ>

Question 8

What is the Pauli exclusion principle?

Answer 8

Two identical fermions cannot coexist in the same quantum state

Question 9

What is the partition function for a many particle system with a single state?

Answer 9

Z=Σe^-nβ(E-μ)
Over n

Question 10

What is the mean occupation number?

Answer 10

< n > =-1/β dlnz/dE

Question 11

What is the distribution function for fermions?

Answer 11

f_F.D.(E)=1/(e^β(E-μ)+1)

Question 12

What is the range of the Fermi-Dirac distribution?

Answer 12

From 0 to 1

Question 13

What is the distribution function for bosons?

Answer 13

f_F.D.(E)=1/(e^β(E-μ)-1)

Question 14

What is the range of the Bose-Einstein distribution ?

Answer 14

From 0 to infinity

Question 15

How is the total number of particles in a system calculated using the distribution function?

Answer 15

N=∫g(E)f(E)dE
From 0 to inifnity

Question 16

How is the interna energy of the system calculated using the distribution function?

Answer 16

U=∫Eg(E)f(E)dE
From 0 to infinity