1. Quantum mechanics II Winter 2012
Physics 452
Quantum mechanics II
Winter 2012
Karine Chesnel

2. Phys 452
Homework
Thursday Jan 12:
assignment #2
5.28, 5.30, 5.31

3. Quantum statistical mechanics
Phys 452
Quantum statistical mechanics
Most probable occupation number:
Distinguishable particle
Identical fermions
Identical bosons

4. Quantum statistical mechanics
Phys 452
Quantum statistical mechanics
Most probable occupation number:
To be determined by E, N
Or by T and characteristic
energy of the system

5. Quantum statistical mechanics
Phys 452
Quantum statistical mechanics
Calculation of a and b:
Case of ideal gas
One spherical shell
Bravais
k-space
Fermi
surface
“degeneracy”
density of states
Volume in k-space
of each individual state

6. Quantum statistical mechanics
Phys 452
Quantum statistical mechanics
Calculation of a and b:
Case of ideal gas : distinguishable particles
We identify
and

7. Quantum statistical mechanics
Phys 452
Quantum statistical mechanics
Meaning of a and b:
Case of ideal gas : distinguishable particles
Using
and

8. Quantum statistical mechanics
Phys 452
Quantum statistical mechanics
Most probable occupation number
or density of occupation:
Distinguishable particle
Maxwell-Boltzmann
distribution
Identical fermions
Fermi- Dirac
distribution
Identical bosons
Bose-Einstein
distribution

9. Quiz 3a Phys 452 What is the maximum possible value
for the density of occupation in case of fermions
at a given temperature T? A. B.
C. 1
D. 0
E. 1/2

10. Quantum statistical mechanics
Phys 452
Quantum statistical mechanics
Fermi-Dirac distribution: if

11. Quantum statistical mechanics
Phys 452
Ideal gas of fermions or bosons
Pb 5.28: Fermions at T=0
Relationships between EF, kF and Etot, N
Bose-Einstein condensation
And all particles condense into ground state
Pb 5.29: Bosons
Predicted in
First measured on Rb atoms 1995
First measured on Photons 2010

12. Quiz 3b Phys 452 What is the maximum possible value
for the density of occupation in case of bosons? A. B.
C. 1
D. 0
E. 1/2

13. Quantum statistical mechanics
Phys 452
Quantum statistical mechanics
Black-body spectrum
Photons
Boson: S=1; m=+/-1
Energy- wavelength:
Non-conservation of the
number of photons (a =0)
Density of energy

14. Quantum statistical mechanics
Phys 452
Quantum statistical mechanics
Black-body spectrum
Wien displacement law
Bosons
at equili-
brium T
Analogy: lava emits light when hot !
Pb 5.30: Wien law
Pb 5.31: Stefan-Boltzmann formula

15. Phys 452
Quiz 3c
We can find that for the blackbody emission, the relationship
between the optimal wavelength and the temperature is
What should be the temperature of the blackbody
to emit principally around 600nm (orange) ?
A. around 2000K
B. around 5000K
C. around 8000K
D. around 10000K
E. around 20000K