1. Physics 452 Quantum mechanics II Winter 2012 Karine Chesnel

2. Physics 452 Homework First homework assignment: Tuesday Jan 10 by 7pm Assignment # 1: Problems 5.22, 5.23, 5.24 in the textbook

3. Phys 452 Quantum statistical mechanics One particle Two particles N particles

4. Quantum statistical mechanics N particles ( ) Thermal equilibrium, T Phys 452 Quantization of the energy for individual particles Total energy:

5. Quantum statistical mechanics N particles ( ) Thermal equilibrium, T What is the probability to find that particle in the particular energy E j ? Phys 452

6. Quantum statistical mechanics Phys 452 3 kind of particles Distinguishable particle Identical fermions Identical bosons Antisymmetric state Symmetric state

7. Quiz 1a Phys 452 Which one of these equalities satisfies the antisymmetrization requirement for a 3- fermions system? A. B. C. D. E. pb 5.22

8. Quantum statistical mechanics Example: 3 –particle system Phys 452 For each type of particles: List all the possible configurations Determine the number of combinations of each configuration Determine the probability for a given individual energy, from all the possible configurations Textbook example Infinite square well In-class example/ pb 5.23 Harmonic oscillator

9. Quiz 1b Phys 452 A. 10 B. 4 C. 1 D. 6 E. 2 Consider 3 distinguishable particles in a harmonic oscillator potential. If the total energy of the system is how many possibilities there are to get the configuration (1,1,1,0,…)?

10. Quiz 1c Phys 452 A. 10 B. 4 C. 1 D. 6 E. 2 Consider 3 fermions particles in a harmonic oscillator potential. If the total energy of the system is how many possibilities there are to get the configuration (1,1,1,0,…)?

11. Quiz 1d Phys 452 A. 10 B. 4 C. 1 D. 6 E. 2 Consider 3 bosons in a harmonic oscillator potential. If the total energy of the system is how many possibilities there are to get the configuration (1,1,1,0,…)?

12. Quantum statistical mechanics Phys 452 Statistical configuration number: Distinguishable particle Identical bosons Work out examples: harmonic oscillator, infinite square well Identical fermions