Analytical and Quantum Mechanics

  • Level of study

    BAC +3

  • ECTS

    7 credits

  • Component

    Faculty of Science

  • Hourly volume

    63h

Description

This UE represents the natural continuation of the UEs of classical Newtonian mechanics.

In the first part of the course, we deal with Classical Mechanics starting from the principle of least action to arrive at two new formulations: the Lagrangian formalism and the Hamiltonian formalism. We study the link between physical symmetries and conservation laws (E. Noether's theorem) and we introduce Poisson's brackets which allow us to write the classical laws of temporal evolution of physical quantities in a form which already prefigures those of quantum mechanics.

In the second part of the course, starting from the examination of the experimental limits of classical mechanics, a new theory of mechanics is introduced: Quantum Mechanics. It is a theory that is conceptually completely different from the previous classical theories, based on a description of physical phenomena in terms of probabilities and therefore no longer deterministic. It is a radical change of paradigm that has shaken up the physics of the last century and has allowed a deeper understanding of physical nature, with fundamental and practical consequences that have radically changed the life of humanity (atomic physics, chemistry, nuclear energy, transistors, LASERS, to name but a few). 

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Objectives

To provide the basic elements of Classical Mechanics in the Lagrangian and Hamiltonian formulations, and to introduce the basic concepts of the new theory of "non-classical" mechanics, i.e. quantum mechanics. This course will allow a first exploration of the quantum world, and will provide the first conceptual and mathematical tools necessary for all quantum physics courses in L3, M1 and M2.

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Necessary pre-requisites

  - Newtonian Mechanics

  - Mathematical Analysis

  - Linear algebra and matrix calculations

  - Electromagnetism

Recommended prerequisites*:

  - Statistical Physics  

   - Analysis and advanced matrix calculation

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Knowledge control

100% CT

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Syllabus

Analytical Mechanics:

  • Variational principle
  • Lagrangian formalism
  • Hamiltonian formalism
  • Symmetries and conservation laws
  • Fish hooks

Quantum Mechanics:

  • Introduction, Planck's formula and solution of the black body problem, photoelectric effect, limits of the classical atomic model, Compton effect
  • QM postulates
  • Wave-particle dualism
  • Schrödinger equation
  • Indeterminacy relations
  • Elements on Hilbert spaces and wave functions
  • Operators
  • Switches
  • One-dimensional problems (barrier/sink/harmonic oscillator)
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Additional information

CM : 31.5 h

TD : 31.5 h

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