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238152 results in Physics and Astronomy

Page 419 of 11908

Fundamentals of Particle Physics
  • Understanding the Standard Model
  • Pascal Paganini
  • Published online:
    31 August 2023
    Print publication:
    14 September 2023
  • This text is a modern introduction to the Standard Model of particle physics for graduate students and advanced undergraduate students. Assuming only prior knowledge of special relativity and non-relativistic quantum mechanics, it presents all aspects of the field, including step-by-step explanations of the theory and the most recent experimental results. Taking a pedagogical, first-principles approach, it demonstrates the essential tools for students to process and analyse experimental particle physics data for themselves. While relatively short compared to other texts, it provides enough material to be covered comfortably in a two-semester course. Some of the more technical details are given in optional supplementary boxes, while problems are provided at the end of each chapter. Written as a bridge between basic descriptive books and purely theoretical works, this text offers instructors ample flexibility to meet the needs of their courses.

  • 4 - Bayesian Inference

  • from Part I - Concepts from Modeling, Inference, and Computing
  • Steve Pressé, Arizona State University, Ioannis Sgouralis, University of Tennessee, Knoxville
  • Book:
    Data Modeling for the Sciences
    Published online:
    17 August 2023
    Print publication:
    31 August 2023, pp 131-162

  • Summary

    In this chapter we introduce Bayesian inference and use it to extend the frequentist models of the previous chapters. To do this, we describe the concept of model priors, informative priors, uninformative priors, and conjugate prior-likelihood pairs . We then discuss Bayesian updating rules for using priors and likelihoods to obtain posteriors. Building upon priors and posteriors, we then describe more advanced concepts including predictive distributions, Bayes factors, expectation maximization to obtain maximum posterior estimators, and model selection. Finally, we present hierarchical Bayesian models, Markov blankets, and graphical representations. We conclude with a case study on change point detection.

  • 9 - Composite Quantum Systems and Entanglement

  • 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 218-247

  • Summary

    The composition of subsystems in quantum theory is defined in terms of a mathematical operation known as the tensor product. We proceed to explain this concept, and to show how it fits in the Hilbert space calculus.

  • 3 - Electron Propagation

  • A. F. J. Levi, University of Southern California
  • Book:
    Applied Quantum Mechanics
    Published online:
    27 October 2023
    Print publication:
    31 August 2023, pp 105-169

  • Summary

    The propagation method can be used to describe a particle with wave character moving in an arbitrary one-dimensional potential, V(x). This is done by approximating the potential as a series of potential steps. For a particle of energy E incident from the left, transmission and reflection at the first step is calculated along with phase accumulated propagating to the step and expressed as a 2×2 matrix.

  • 6 - Science as a Social Endeavor

  • David B. Teplow, University of California, Los Angeles
  • Book:
    The Philosophy and Practice of Science
    Published online:
    17 September 2023
    Print publication:
    31 August 2023, pp 302-346

  • Summary

    Science always has occupied a special niche in society because of its perceived and proven truth value, which comes from its ostensibly unbiased, rigorous, accurate, precise, dispassionate, and metaphysical nature. After all, isn't science practiced in laboratories and universities quite apart from the "real world," the world of opinion, supposition, business, politics, and religion? But is it? As discussed in this chapter, the answer is "no," because science, in many senses, is a social endeavor, one subject to the vagaries of personal bias, the quest for recognition and funding, peer and social pressure, and tradition. Science may indeed be special relative to other endeavors, but this does not mean that its product – knowledge – should be accepted without question. Science can be wrong, but only temporarily, as it is a self-correcting enterprise that, in light of continual hypothesis testing, eventually fixes its own errors.

  • 7 - Time Evolution

  • 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 169-198

  • Summary

    In Chapter 2, we saw that the nascent quantum theory was divided between two different descriptions of time evolution.

  • 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.

Page 419 of 11908