Quantum physics, Analytical mechanics, Special relativity

Description

Elements of analytical mechanics, quantum mechanics and special relativity

• Analytical mechanics :
  • Euler-Lagrange equation, generalized coordinates, constant of the motion, Lagrange constraints and multipliers.
  • From Lagrandian to Hamiltonian, Hamilton equations, Poisson brackets, canonical transformations.
  • Varationional principle, conservation laws, Noether’s theorem.
  • Lagrangian description of continuous media.

• Quantum mechanics :
  • Postulates, Schrödinger equation, observables and corresponding operators.
  • Coupling of orbital moment, perturbation theory, varationional method.
  • Density matrix, second quantification.

• Special relativity for subatomic physics :
  • Postulates, Lorentz transformations, Minkowski space, lengths contraction and time dilation.
  • Energy-monentum quadrivectors and relativistic kinematics.
  • Dirac equations, derivation, formulation with gamma-matrices and solutions.

Compétences visées

•    Applying knowledge in physics

•    Apply methods from mathematics and digital technology

•    Produce a critical analysis, with hindsight and perspective

•    Interact with colleagues in physics and other disciplines

•    Develop and manage an experimental project, including digital aspects

•    Operate an experimental device, including digital aspects, from use to data analysis

•    Take on responsibilities in a team working on an experimental project

•    Research a physics topic using specialised resources

•    Communicate in writing and orally, including in English

•    Contribute to research work in physics

•    Respect ethical, professional and environmental principles in the practice of physics 

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