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

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

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

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

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

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

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

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

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

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

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 1924-25 First measured on Rb atoms 1995 First measured on Photons 2010

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

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

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

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