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26203 results in Theoretical Physics and Mathematical Physics

Page 41 of 1311

  • Chapter 3 - Bra-ket Notation

  • Michael Wick, Hochschule Coburg, Germany
  • Book:
    Quantum Mechanics with Concept Maps
    Published online:
    07 September 2023
    Print publication:
    21 September 2023, pp 67-94

  • Summary

    The state of a quantum-mechanical system can be described by a wave function or a state ket. Each wave function is defined in a specific space (e.g. in the position or momentum space). Conversely, the state kets do not require a specific space. The terms ‘bra’ and ‘ket’ are derived from the word ‘bracket’.

  • 2 - Preliminary Concepts: Special Relativity and Quantum Mechanics

  • Pascal Paganini, École Polytechnique, Paris
  • Book:
    Fundamentals of Particle Physics
    Published online:
    31 August 2023
    Print publication:
    14 September 2023, pp 56-78

  • Summary

    A good knowledge of special relativity and quantum mechanics is essential for studying particle physics. Even if the reader is assumed to be already familiar with these two theories, a brief review of special relativity is given in this chapter with emphasis on the covariant and contravariant notations, which may be less well mastered but are very useful in particle physics. Important aspects of quantum mechanics for particle physics, such as the angular momentum, are also addressed.

  • 3 - Collisions and Decays

  • Pascal Paganini, École Polytechnique, Paris
  • Book:
    Fundamentals of Particle Physics
    Published online:
    31 August 2023
    Print publication:
    14 September 2023, pp 79-100

  • Summary

    The determination of particle properties relies mostly on experimental measurements based on their collisions and decays. This chapter introduces the concepts of reaction cross section and particle decay rate. For unstable particles, the origin of its lifetime as well as the notion of branching ratios is presented. Many formulas involving the reactions between two particles are derived in detail, and phase spaces involving three-body decays are presented with Dalitz diagrams. The notion of cross reactions is also presented.

Page 41 of 1311