lecturenotes:bestof []

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==== Best of PhiSX ====

Students have to master an increasingly larger and complex body of knowledge. Being more selective on the material is only one way to cope with this problem. Clarifying the presentation of concepts and simplifying their notation has always been key to the advancement of science. Text books and lecture notes such as PhiSX are one effort in this direction. The goal is that teachers will make use of good explanations or teaching methods, use them and thus spread them. On this page, I will point out my personal views of what worked well. Some of it is novel, others not.

The following list is neither ranked nor ordered.

    - **Entropy**: Build statistical physics and thermodynamics on the concept of information theory, speak Shannon's entropy and the maximum-entropy principle. (Statistical Physics)
    - **Probability**: I adhere to the subjective interpretation of probabilities, meaning that probabilities describe, at first, the observers state of mind. This avoids the conceptual difficulties of the collapse of the probability distribution and of the fact that observers may use different probability distributions, when they have access to different observations.  (Statistical Physics)
    - **Ensembles**: The concept of an ensemble is introduced in a general form as a set of states and their probabilities. Thermal ensembles such as the canonical ensemble are derived via the maximum-entropy principle. 
   - Motivate **quantum mechanics**: The double-slit experiment establishes the wave aspect of particles. The dynamics of wave packets is introduced for a general classical field theory. The requirement that wave packets behave on a macroscopic scale like classical particles leads to the correspondence principle and the Schrödinger equation. (Quantum Theory)
   - **Noether theorem**: Noether theorem links symmetries with conservation laws. I derive Noethertheorem, in its general form once for particles and once for fields rather than individually for selected conservation laws such as as energy, momentum and angular momentum. The general form makes the special role of energy and momentum evident. (Klassische Mechanik, Elektrodynamik)
  - **Thermodynamic limit**: The micro-canonical, canonical and grand-canonical ensembles are usually defined as having sharp values for the energy and particle number. With this definition, the formalism of thermodynamics is consistent only in the thermodynamic limit, that is for infinite large systems, where the relative fluctuations vanish. I define ensembles as having defined thermal expectation values of energy and particle number. As a result the thermodynamic relations can be applied for arbitrary small systems as well.
  - **Band structures**: I use a simple 2-dimensional tight-binding model on a square lattice with atoms having s and p-electrons in the plane to construct the band structure graphically. This connects Bloch theorem with local orbitals. Then I show the relation to a free electron gas on the same lattice. (Introduction to Solid-State Theory)
  - **Down-folding**: I describe quantum systems in contact to introduce the concept of a self energy and to motivate many-particle Green's functions. (Advanced Solid State Theory)
  - **Hyperlinks**: Using LaTeX it is straightforward to hyperlink equations, so that students quickly find the prerequisites of a step in the derivation. 
  - Quantum mechanical **measurement process**: Decoherence as process underlying the measurement process.
  - Consistent framework to divide the system into **phonons**, electronic excitations, electron-phonon coupling, phonon scattering etc. (Introduction to Solid State Theory)
  - ...