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3120 results in Quantum Physics, Quantum Information and Quantum Computation

Page 21 of 156

  • 4 - Operators I

  • from Part II - The Principles of Quantum Theory
  • Charis Anastopoulos, University of Patras, Greece
  • Book:
    Quantum Theory
    Published online:
    06 October 2023
    Print publication:
    31 August 2023, pp 75-104

  • Summary

    Given the description of a quantum state in terms of Hilbert space vectors, physical magnitudes (Heisenberg’s matrices) correspond to linear operators on the Hilbert space. A linear operator (or simply, operator) is a linear map of a Hilbert space to itself.

  • 2 - Using the Schrödinger Wave Equation

  • A. F. J. Levi, University of Southern California
  • Book:
    Applied Quantum Mechanics
    Published online:
    27 October 2023
    Print publication:
    31 August 2023, pp 55-104

  • Summary

    According to the Schrödinger equation, a particle with wave character and mass m in the presence of a potential may be described as a state that is a function of space and time. Space and time are assumed to be smooth and continuous. The potential can localize the particle to one region of space forming a bound state.

  • 19 - Scattering Theory

  • from Part IV - Techniques
  • Charis Anastopoulos, University of Patras, Greece
  • Book:
    Quantum Theory
    Published online:
    06 October 2023
    Print publication:
    31 August 2023, pp 496-536

  • Summary

    Scattering experiments are one of our most important tools for extracting information about the structure and interactions of microscopic systems. In these experiments, we prepare a beam of particles of a given type and we direct it towards a target. The interaction of the particles in the beam with those of the target may lead to various phenomena: changes in the direction and the energy of incoming particles, absorption of incoming particles, the appearance of new species of particles, and so on. The target is surrounded by particle detectors that identify the particles that exit the interaction region and measure their momenta.

  • 21 - Quantum Measurements

  • from Part V - Quantum Foundations
  • Charis Anastopoulos, University of Patras, Greece
  • Book:
    Quantum Theory
    Published online:
    06 October 2023
    Print publication:
    31 August 2023, pp 569-593

  • Summary

    In previous chapters, we saw that quantum theory is unique among physical theories, in that its predictions refer exclusively to measurement outcomes rather than to the properties of physical objects. It is therefore no surprise that the study of quantum measurements has developed into a research field on its own. The earlier studies of quantum measurements focused on conceptual and foundational issues, but in recent years quantum measurement theory has become a crucial tool for quantum technologies.

  • 4 - Eigenstates and Operators

  • A. F. J. Levi, University of Southern California
  • Book:
    Applied Quantum Mechanics
    Published online:
    27 October 2023
    Print publication:
    31 August 2023, pp 170-224

  • Summary

    Quantum mechanics is a very successful description of atomic scale systems. The mathematical formalism relies on the algebra of noncommuting linear Hermitian operators. Postulates provide a logical framework with which to make contact with the results of experimental measurements.

  • 11 - Symmetries I

  • from Part III - Elementary Systems and Their Symmetries
  • Charis Anastopoulos, University of Patras, Greece
  • Book:
    Quantum Theory
    Published online:
    06 October 2023
    Print publication:
    31 August 2023, pp 273-304

  • Summary

    In previous chapters, we encountered the fundamental principles of quantum theory and we saw how the representation of physical magnitudes by Hilbert space operators allows us to construct probabilities for the outcome of any experiment. However, these principles do not tell us what the fundamental physical systems are, how to construct their associated Hilbert spaces, and which operators correspond to physical magnitudes.

Page 21 of 156