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Quantum and statistical physics

Presentation

Programme (detailed contents):

A : Quantum Physics

v  Brief recall on wavefunction formalism and introduction to Dirac formalism

v  Fundamental postulates concerning Observables and their Measurement

v  Dynamics of quantum systems

v  Theory of the harmonic oscillator

v  Theory of Angular momentum

B : Statistical Physics

v  Fundamental hypotheses of statistical physics. Macroscopic states, microscopic states and state density.

v  Closed systems in equilibrium, micro-canonical distribution. Statistical temperature and Boltzmann distribution. Z, U and S functions. Link with thermodynamics

v  Closed systems in contact with a thermostat, canonical distribution.

v  Closed systems in contact with a particle reservoir, grand canonical distribution. Chemical potential.

v  Fermions and Bosons. Fermi-Dirac and Bose-Einstein distribution. Application examples.

Organisation:

v  part A will be followed by part B

v  Part A: 1 teacher for lectures and 1 teacher for tutorials

v  Part B: 2 teachers for lectures and 2 teachers for tutorials

Main difficulties for students:

Difficulties essentially due to mathematics (new formalism, diagonalising of matrices..), statistics.

Objectives

 

At the end of this module, the student will have understood and be able to explain (main concepts):

v  Fundamentals concerning Observables and their Measurement

v  The temporal evolution of a quantum system. Plane waves and wave packets

v  Theory of the harmonic oscillator and applications

v  Theory of Angular momentum and applications

v  The fundamental principles of statistical physics (entropy)

v  Micro-canonical distribution, temperature, partition function and U, S functions.

v  Canonical and grand canonical distribution.

v  Fermi-Dirac and Bose-Einstein distributions

The student will be able to:

v  Solve the Schrödinger equation (eigenvalues and eigenstates) using matrix formalism

v  Apply postulates concerning Observables and their Measurement

v  Calculate the temporal evolution of a quantum state

v  Manipulate operators for the harmonic oscillator and angular momentum

v  Calculate the equilibrium properties of simple closed and open systems.

Use the Fermi-Dirac or Bose-Einstein distribution in solid state physics.

Needed prerequisite

Matrix Calculations (eigenvalues, eigenstates, diagonalization,), second order differential equations, Integral calculations. Basics on quantum mechanics in the wave-function formalism.
Probability and statistical mathematics.

Form of assessment

The evaluation of outcome prior learning is made as a continuous training during the semester. According ot the teaching, the assessment will be different: as a written exam, an oral exam, a record, a written report, peers review...

Benefits

Mécanique Quantique (Tome I et II) C. Cohen-Tanoudji, B. Diu, F. Laloë, chez Hermann (1977)

Mecanique quantique J.L Basdevant et J. Dalibard, édition de l'Ecole Polytechnique (2004)

CD-Rom M. Joffre (Ecole Polytechnique, 2004)

Physique Statistique B. Diu, C Guthmann, D. Lederer, B. Roulet, chez Hermann (1989)

Thermodynamique J.P Pérez chez Masson (1997)