Mathematical formulation of quantum mechanicsThe mathematical formulations of quantum mechanics are those mathematical formalisms that permit a rigorous description of quantum mechanics. This mathematical formalism uses mainly a part of functional analysis, especially Hilbert spaces, which are a kind of linear space. Such are distinguished from mathematical formalisms for physics theories developed prior to the early 1900s by the use of abstract mathematical structures, such as infinite-dimensional Hilbert spaces (L2 space mainly), and operators on these spaces.
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.
RidgeA ridge is a long, narrow, elevated geomorphologic landform, structural feature, or combination of both separated from the surrounding terrain by steep sides. The sides of a ridge slope away from a narrow top, the crest or ridgecrest, with the terrain dropping down on either side. The crest, if narrow, is also called a ridgeline. Limitations on the dimensions of a ridge are lacking. Its height above the surrounding terrain can vary from less than a meter to hundreds of meters.
BASICBASIC (Beginners' All-purpose Symbolic Instruction Code) is a family of general-purpose, high-level programming languages designed for ease of use. The original version was created by John G. Kemeny and Thomas E. Kurtz at Dartmouth College in 1963. They wanted to enable students in non-scientific fields to use computers. At the time, nearly all computers required writing custom software, which only scientists and mathematicians tended to learn.
Computer simulationComputer simulation is the process of mathematical modelling, performed on a computer, which is designed to predict the behaviour of, or the outcome of, a real-world or physical system. The reliability of some mathematical models can be determined by comparing their results to the real-world outcomes they aim to predict. Computer simulations have become a useful tool for the mathematical modeling of many natural systems in physics (computational physics), astrophysics, climatology, chemistry, biology and manufacturing, as well as human systems in economics, psychology, social science, health care and engineering.
Mathematical physicsMathematical physics refers to the development of mathematical methods for application to problems in physics. The Journal of Mathematical Physics defines the field as "the application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and for the formulation of physical theories". An alternative definition would also include those mathematics that are inspired by physics (also known as physical mathematics).
Beach nourishmentBeach nourishment (also referred to as beach renourishment, beach replenishment, or sand replenishment) describes a process by which sediment, usually sand, lost through longshore drift or erosion is replaced from other sources. A wider beach can reduce storm damage to coastal structures by dissipating energy across the surf zone, protecting upland structures and infrastructure from storm surges, tsunamis and unusually high tides. Beach nourishment is typically part of a larger integrated coastal zone management aimed at coastal defense.
Microsoft BASICMicrosoft BASIC is the foundation software product of the Microsoft company and evolved into a line of BASIC interpreters and compiler(s) adapted for many different microcomputers. It first appeared in 1975 as Altair BASIC, which was the first version of BASIC published by Microsoft as well as the first high-level programming language available for the Altair 8800 microcomputer. During the home computer craze during the late-1970s and early-1980s, BASIC was ported to and supplied with many home computer designs.
NamibThe Namib (ˈnɑːmɪb ; Namibe) is a coastal desert in Southern Africa. According to the broadest definition, the Namib stretches for more than along the Atlantic coasts of Angola, Namibia, and South Africa, extending southward from the Carunjamba River in Angola, through Namibia and to the Olifants River in Western Cape, South Africa. The Namib's northernmost portion, which extends from the Angola-Namibia border, is known as Moçâmedes Desert, while its southern portion approaches the neighboring Kalahari Desert.
Phase-space formulationThe phase-space formulation of quantum mechanics places the position and momentum variables on equal footing in phase space. In contrast, the Schrödinger picture uses the position or momentum representations (see also position and momentum space). The two key features of the phase-space formulation are that the quantum state is described by a quasiprobability distribution (instead of a wave function, state vector, or density matrix) and operator multiplication is replaced by a star product.
