FYTA12, statistical part
Schedule
For this part, the lectures are marked with S, the exercises with ÖS, and the SI sessions with SIS in the course schedule.
It consists of two parts:
(S1) Statistical Mechanics (6 hp, given first part of semester),
(S2) Quantum Mechanics (9 hp, given last part of semester).
Literature
Swedish: H.-U. Bengtsson och Patrik Edén (reviderad 2:a uppl.), Grundläggande statistisk fysik och kvantmekanik (for sale at the Theoretical Physics expedition).
(English alternative: to be decided, if needed.)
Weekly planning for vt 2016 (preliminary)
Statistical mechanics part (6 hp)
- w 3.
- Chpts. 1–3: State variables, entropy, the Boltzmann factor, closed vs. open systems.
- w 4.
- Chpts. 4–5: Partition function, free energy.
- w 5.
- Chpts. 6–8: Heat machines, heat capacity, the equipartition principle, black body radiation.
- w 6.
- Chpts. 9–10: The quantum hypothesis, wave-particle dualism.
(Laboration: Normal modes.) - w 7.
- Chpts. 11–12: Heat capacities in quantum systems, identical particles.
- w 8.
- Chpts. 13–14: Degenerate fermion or boson gases.
(Laboration: Rubber band.) - w 9.
- Leftovers and repetition.
- w 10.
- Repetition. Exam.
Quantum mechanics part (9 hp)
- w 11.
- Chpts. 15–18: Operators, states, Schrödinger eq., 1-D box.
- w 13.
- Chpts. 19–22: Parity, id. particles, piecewise const. pot.,
Mickey Mouse crystal, tunnelling.
(Computer exercise: Bose-Einstein condensation) - w 14.
- Chpts. 23–24: Linear algebra, measurements, indeterminacy.
- w 15.
- Chpts. 25–26: The harmonic oscillator. Static perturbation theory.
- w 16.
- Chpts. 27–28: Time-dependent perturbation theory. Scattering.
- w 17.
- Chpts. 29–30: 3-D SE, angular momentum, gen. ang. mom.
- w 18.
- Chpt. 31: Radial SE. Hydrogen atom. Spin.
(Computer exercise: Scattering) - w 19.
- Chpts. 32–34: Spin and its representations; spin in arb. directions
- w 20.
- Chpts. 35–36: Addition of angular momenta. Bell's inequalities.
- w 21.
- Leftovers and repetition. Exam.
Distributed notes etc.
Statistical mechanics
- Overview of the statistical mechanics part
- Answers to exercises
- Gamla tentauppgifter och svar.
- Gammal tenta -12 (120228) med svar.
- Gammal tenta -13 (130301).
- Gammal tenta -14 (140307).
- Gammal tenta -15 (150306).
Quantum mechanics
- Overview of the quantum mechanics part
- Answers to exercises
- Extra övningsuppgifter i kvantmekanik, med kortfattad facit.
- Gamla tentauppgifter, med svar.
- Gammal tenta -12 (120601).
- Gammal tenta -13 (130530).
- Gammal tenta -14 (140605).
- Gammal tenta -15 (150529).
Exercises
All exercises in HUB/PE are suitable for training purposes, and the correct answers for some of them are given above.
Tasks treated on exercise sessions
Statistical mechanics
Quantum mechanics
- w13.
- 15.1, 16.4, 18.3, 20.2, 22.2, 22.4
- w16.
- 23.1, 24.6, 25.5, 26.3
- w17.
- Hemgjord uppgift BS-25, 29.1, 30.1, 30.2
- w19.
- 33.2, 33.4, 34.1, 34.2, 34.4
Hand-in tasks
Solution to be handed in before the following Thursday at 1:15 PM (unless otherwise stated). The tasks should be solved individually, and the solutions should be written in a nice and easily readable manner, or typeset using a computer.Statistical physics
- w5.
- Exercise 5.6 in the book.
- w7.
- Exercise 8.2 in the book.
- w9.
- Exercise 12.3 in the book.
Quantum mechanics
- w14.
- Exercise 20.5
- w17.
- Exercise 26.2
- w18.
- Exercise 28.1
- w20.
- Exercise 34.2
Various messages
Fel och oklarheter etc. i HUB/PE:- Uppg. 27.2: Felaktigt uttryck för pmax2/c2 i slutet av
del (c), ska vara:
((mn2 − mp2 − me2)2 − 4 mp2me2) / (4 mn2).
Additional reading
F. Mandl, Statistical Physics (Wiley, 2nd ed.).
B.H. Bransden och C.J. Joachain, Introduction to Quantum Mechanics (Longman Scientific and Technical, 2nd ed.).
J.J. Sakurai, Modern Quantum Mechanics (Addison-Wesley).