Physics 452 Quantum mechanics II Winter 2012 Karine Chesnel

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

Phys 452 Quantum statistical mechanics One particle Two particles N particles

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

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

Quantum statistical mechanics Phys kind of particles Distinguishable particle Identical fermions Identical bosons Antisymmetric state Symmetric state

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

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

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,…)?

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,…)?

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,…)?

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