Quantum Mechanics and

Statistical Physics

Time period: Qt I
Module: 1+ 6
Language: Swedish/English
Examiner: Hans Weber Univ lekt
Prerequisite: Modern Physics, Optics, Electromagnetic field theory and Mechanics, Physics 1,2 and 3. Mathematics vector calculus and series complex functions and the theory of transformations.
Course aim: To give an introduction to Quantum Mechanics and Statistical Mechanics and there calculational technics. After the course, the student should be able to understand and apply:
- The motivation for quantum mechanics in modern physics.
- The foundations of quantum mechanics.
- Wave-particle dualism, wave packet, probability interpretation, Heisenberg uncertanty relations.
- Operators, eigenvalues and expectationvalues.
- Properties of quantum mechanical systems and processes.
- Angular momentum and central motion.
- Fundamental assumptions in Statistical mechanics.
- The three canonical ensembles and central concepts like entropy, Helmholtz and Gibbs free energy.
Contents

Failure of classical physics.
The Schrödinger equation.
Systems with R2 and R3 symmetry.
Eigenstates and eigenvalues.
Applications of quantum physics to several cases like the Hydrogen atom, the Harmonic oscillator.
Spin.
Ergodic assumption, partitionfunction, entropy.
Temperature.
Micro caononical, canonical and grand canonical ensembles, reversability,
Ideal gas (kinetic gastheory), Maxwell-Boltzmann distribution.
Fermi and Bose statistics, free energy, mean field theory.

Teaching: The education consists of lectures, home assignements and lab exercises.
Examination: Written examination at the end of the course, and written lab reports.
Course grade scale: U, 3, 4, 5
Literature:

B. H. Bransden & C. J. Joachain, Quantum Mechanics 2ed 2000, Prentice Hall ISBN 0582-35691-1.
Charles Kittel and Herber Kroemer, Thermal Physics 2ed 1980, Freeman and Company ISBN 0-7167-1088-9.
Written material on Molecules, Spin, Statistical physics

Remarks: This course can not be combined with the following courses MTF067, MTF057, MTF072, MTF107, MTF115 and MTF131. If required lectures can be given in English.
http://www.mt.luth.se/~weber/kurs/kvant_statmek/kursprog.html

Teacher: Hans Weber ,Tel 0920-492088, 0708-592088, Office: E111

Lecture	Contents	Kapitel	Sidor	Exercises
Q1	Introduction to quantum mechanics.	Ch 1	1 - 45	E1, E17, 1.5, 1.7, 1.8, 1.11, 1.12, 1.15, 1.22, 1.25, 1.27
Q2	Wave description of matter.	Ch 2	51 - 76	2.1, 2.9, 2.10, 2.12, 2.13
Q3-4	Schrödinger equation.	Ch 3.1-3.8	66 - 124	3.2, 3.12, E2, E3, E4, E5, E6, E21
Q5-6	One dimension	Ch 4.1-4.7	133 - 182	4.3, 4.4, 4.5, 4.6, 4.7, 4.12, 4.17, E2, E3, E4, E5, E6, E7, E23, E24
Q7 (S)	problem solving			E25, E26, E27
Q8	Some Formalism	Ch 5.1-5.4	193 - 216	5.1, 5.2, 5.3, 5.9, E10, E11, E12
Q9-10	Angular momentum, spin	Ch 6.1, 6.3, 6.5, 6.8 + handout	265 - 322	6.1, 6.11, 6.15, 6.17, 6.18a, 6.19, E9, E14, E15, E16
Q11 (S)	Problem solving
Q12-13	Three dimensions	Ch 7.1-7.5	327-367	7.1, 7.2, 7.7, 7.10, 7.18, 7.20
Q14	Many identical particles	Ch 10.1-10.3	469 - 485	10.2, 10.3
Q15 (S)	Review, Problem solving

S1	States of a model system	Ch 1-2	5-42	-
S2	Entropy and Temperature Boltzmann distribution and Helmholtz free energy,	Ch2-3	42-51,58-80	2.1, 2.2, 2.3 3.1, 3.2, 3.3, 3.4, 3.8, 3.11
S3	Thermal Radiation and Planck Distribution	Ch 4 (not 99-102)		4.1, 4.2, 4.4, 4.5, 4.11
S4	Chemical Potential and Gibbs distribution	Ch 5		5.3, 5.5, 5.6, 5.7, 5.8, 5.9, 5.11, 5.12, 5.13, 5.14
S5	Ideal Gas, Chapter 6	Ch 6		6.1, 6.2, 6.3, 6.6, 6.10, 6.12, 6.15
S6	Fermi and Bose gases	Ch 7		7.1, 7.2, 7.3, 7.7, 7.8, 7.9