Matrix mechanics

Matrix mechanics is a formulation of quantum mechanics created by Werner Heisenberg, Max Born, and Pascual Jordan in 1925. It was the first conceptually autonomous and logically consistent formulation of quantum mechanics. Its account of quantum jumps supplanted the Bohr model's electron orbits. It did so by interpreting the physical properties of particles as matrices that evolve in time. It is equivalent to the Schrödinger wave formulation of quantum mechanics, as manifest in Dirac's bra–ket notation. In some contrast to the wave formulation, it produces spectra of (mostly energy) operators by purely algebraic, ladder operator methods. Relying on these methods, Wolfgang Pauli derived the hydrogen atom spectrum in 1926, before the development of wave mechanics. Development of matrix mechanics In 1925, Werner Heisenberg, Max Born, and Pascual Jordan formulated the matrix mechanics representation of quantum mechanics. Epiphany at Helgoland In 1925 Werner Heisenb

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Momentum space CFT correlators for Hamiltonian truncation

Matthew Thomas Walters

We consider Lorentzian CFT Wightman functions in momentum space. In particular, we derive a set of reference formulas for computing two- and three-point functions, restricting our attention to three-point functions where the middle operator (corresponding to a Hamiltonian density) carries zero spatial momentum, but otherwise allowing operators to have arbitrary spin. A direct application of our formulas is the computation of Hamiltonian matrix elements within the framework of conformal truncation, a recently proposed method for numerically studying strongly-coupled QFTs in real time and infinite volume. Our momentum space formulas take the form of finite sums over F-2(1) hypergeometric functions, allowing for efficient numerical evaluation. As a concrete application, we work out matrix elements for 3d phi (4)-theory, thus providing the seed ingredients for future truncation studies.

2020

A generalization of the Solis-Wets method

In this paper we focus on the application of global stochastic optimization methods to extremum estimators. We propose a general stochastic method the master method which includes several stochastic optimization algorithms as a particular case. The proposed method is sufficiently general to include the Solis-Wets method, the improving hit-and-run algorithm, and a stochastic version of the zigzag algorithm. A matrix formulation of the master method is presented and some specific results are given for the stochastic zigzag algorithm. Convergence of the proposed method is established under a mild set of conditions, and a simple regression model is used to illustrate the method. (C) 2011 Elsevier B.V. All rights reserved.

Elsevier2012

USSR: An UltraSound Sparse Regularization framework

Marcel Arditi, Adrien Georges Jean Besson, Florian Martinez, Dimitris Perdios, Jean-Philippe Thiran, Yves Wiaux

Ultrafast ultrasound (US) imaging uses unfocused waves to insonify the whole medium of interest at once, allowing pulse-echo US imaging to achieve very high frame rates, at the cost of a lower image quality. In this paper, we present USSR, an UltraSound Sparse Regularization framework which permits high-quality imaging at fast rates and with a very low memory footprint. The framework, based on highly parallelizable, parametric, matrix-free formulations of the measurement model and its adjoint as well as on well-chosen sparsity priors, is implemented on multi-threaded architectures and evaluated on the publicly available PICMUS dataset.

Ieee2017

Quantum mechanics

Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quan

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In quantum physics, a wave function (or wavefunction), represented by the Greek letter Ψ, is a mathematical description of the quantum state of an isolated quantum system. In the Copenhagen interpr

Werner Heisenberg

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Le but du cours de Physique générale est de donner à l'étudiant les notions de base nécessaires à la compréhension des phénomènes physiques. L'objectif est atteint lorsque l'étudiant est capable de prévoir quantitativement les conséquences de ces phénomènes avec des outils théoriques appropriés.