Path integral formulationThe path integral formulation is a description in quantum mechanics that generalizes the action principle of classical mechanics. It replaces the classical notion of a single, unique classical trajectory for a system with a sum, or functional integral, over an infinity of quantum-mechanically possible trajectories to compute a quantum amplitude. This formulation has proven crucial to the subsequent development of theoretical physics, because manifest Lorentz covariance (time and space components of quantities enter equations in the same way) is easier to achieve than in the operator formalism of canonical quantization.
Quantum mechanicsQuantum 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 quantum physics including quantum chemistry, quantum field theory, quantum technology, and quantum information science. Classical physics, the collection of theories that existed before the advent of quantum mechanics, describes many aspects of nature at an ordinary (macroscopic) scale, but is not sufficient for describing them at small (atomic and subatomic) scales.
Virtual particleA virtual particle is a theoretical transient particle that exhibits some of the characteristics of an ordinary particle, while having its existence limited by the uncertainty principle. The concept of virtual particles arises in the perturbation theory of quantum field theory where interactions between ordinary particles are described in terms of exchanges of virtual particles. A process involving virtual particles can be described by a schematic representation known as a Feynman diagram, in which virtual particles are represented by internal lines.
Cloud computingCloud computing is the on-demand availability of computer system resources, especially data storage (cloud storage) and computing power, without direct active management by the user. Large clouds often have functions distributed over multiple locations, each of which is a data center. Cloud computing relies on sharing of resources to achieve coherence and typically uses a pay-as-you-go model, which can help in reducing capital expenses but may also lead to unexpected operating expenses for users.
S-matrixIn physics, the S-matrix or scattering matrix relates the initial state and the final state of a physical system undergoing a scattering process. It is used in quantum mechanics, scattering theory and quantum field theory (QFT). More formally, in the context of QFT, the S-matrix is defined as the unitary matrix connecting sets of asymptotically free particle states (the in-states and the out-states) in the Hilbert space of physical states.
History of AlagoasThe history of Alagoas begins before the discovery of Brazil by the Portuguese, when the territory was inhabited by the Caeté people. The coast of the current state of Alagoas, recognized since the first Portuguese expeditions, was also visited early on by vessels of other nationalities for the barter of brazilwood (Caesalpinia echinata). Within the Captaincies of Brazil system (1534), the territory was part of the captaincy of Pernambuco, and its occupation dates back to the foundation of the village of Penedo (1545), on the banks of the São Francisco River, by the donee Duarte Coelho Pereira, who encouraged the construction of sugar cane mills in the region.
Mafra, PortugalMafra (ˈmafɾɐ) is a city and a municipality in the district of Lisbon, on the west coast of Portugal, and part of the urban agglomeration of the Greater Lisbon subregion. The population in 2011 was 76,685, in an area of 291.66 km2. It is mostly known for the sumptuous Mafra National Palace inscribed as a UNESCO World Heritage Site. Built in the baroque style, the Mafra National Palace also inspired Portuguese Nobel Prize laureate José Saramago to write his novel Baltasar and Blimunda (Memorial do Convento).
Hamiltonian (quantum mechanics)In quantum mechanics, the Hamiltonian of a system is an operator corresponding to the total energy of that system, including both kinetic energy and potential energy. Its spectrum, the system's energy spectrum or its set of energy eigenvalues, is the set of possible outcomes obtainable from a measurement of the system's total energy. Due to its close relation to the energy spectrum and time-evolution of a system, it is of fundamental importance in most formulations of quantum theory.
Windows XPWindows XP is a major release of Microsoft's Windows NT operating system. It was released to manufacturing on August 24, 2001, and later to retail on October 25, 2001. It is a direct upgrade to its predecessors, Windows 2000 for high-end and business users and Windows Me for home users, and is available for any devices running Windows NT 4.0, Windows 98, Windows 2000, or Windows Me that meet the new Windows XP system requirements.
MacOSmacOS (ˌmækoʊˈɛs; previously OS X and originally Mac OS X) is an operating system developed and marketed by Apple Inc. since 2001. It is the primary operating system for Apple's Mac computers. Within the market of desktop and laptop computers, it is the second most widely used desktop OS, after Microsoft Windows and ahead of Linux (including ChromeOS). macOS succeeded the classic Mac OS, a Mac operating system with nine releases from 1984 to 1999.
Windows XP editionsWindows XP, which is the next version of Windows NT after Windows 2000 and the successor to the consumer-oriented Windows Me, has been released in several editions since its original release in 2001. Windows XP is available in many languages. In addition, add-ons translating the user interface are also available for certain languages. The first two editions released by Microsoft are Windows XP Home Edition, designed for home users, and Windows XP Professional, designed for business and power users.
Particle in a ringIn quantum mechanics, the case of a particle in a one-dimensional ring is similar to the particle in a box. The Schrödinger equation for a free particle which is restricted to a ring (technically, whose configuration space is the circle ) is Using polar coordinates on the 1-dimensional ring of radius R, the wave function depends only on the angular coordinate, and so Requiring that the wave function be periodic in with a period (from the demand that the wave functions be single-valued functions on the circle), and that they be normalized leads to the conditions and Under these conditions, the solution to the Schrödinger equation is given by The energy eigenvalues are quantized because of the periodic boundary conditions, and they are required to satisfy or The eigenfunction and eigenenergies are where Therefore, there are two degenerate quantum states for every value of (corresponding to ).
