While the idea of shared electron pairs provides an effective qualitative picture of covalent bonding, quantum mechanics is needed to understand the nature of these bonds and predict the structures and properties of simple molecules.

While the diagrams are applied primarily to quantum field theory, they can also be used in other fields, such as solid-state theory.

While Maxwell's equations are consistent within special and general relativity, there are some quantum mechanical situations in which Maxwell's equations are significantly inaccurate: including extremely strong fields ( see Euler – Heisenberg Lagrangian ) and extremely short distances ( see vacuum polarization ).

While this is extremely easy to implement on sufficiently simple theories, there are many situations where other methods of quantization yield more efficient procedures for computing quantum amplitudes.

* While the seemingly " exotic " behavior of matter posited by quantum mechanics and relativity theory become more apparent when dealing with particles of extremely small size or velocities approaching the speed of light, the laws of classical Newtonian physics remain accurate in predicting the behavior of the vast majority of " large " objects ( on the order of the size of large molecules or bigger ) at velocities much smaller than the velocity of light.

While clearly contributing to the field, he did not accept many of the more " philosophical consequences and interpretations " of quantum mechanics, such as the lack of deterministic causality.

While quantum mechanics primarily applies to the atomic regimes of matter and energy, some systems exhibit quantum mechanical effects on a large scale-superfluidity, the frictionless flow of a liquid at temperatures near absolute zero, is one well-known example.

While a classical three-bit state and a quantum three-qubit state are both eight-dimensional vectors, they are manipulated quite differently for classical or quantum computation.

While confirming that quantum mechanics and gravity are indeed consistent at reasonable energies, it is clear that near or above the fundamental cutoff of our effective quantum theory of gravity ( the cutoff is generally assumed to be of the order of the Planck scale ), a new model of nature will be needed.

While it is true that a bipartite quantum state must be entangled in order for it to produce non-local correlations, there exist entangled states that do not produce such correlations.

While the letter Q in the 8th edition only listed the letter Q itself, the 11th edition also listed quantum satis, quenell, quilt and quisling.

While the results were not surprising since gravity was known to act on everything, including light ( see tests of general relativity and the Pound-Rebka falling photon experiment ), the self-interference of the quantum mechanical wave of a massive fermion in a gravitational field had never been experimentally confirmed before.

While temporarily at the University of Copenhagen, German physicist Werner Heisenberg formulated his famous Uncertainty principle, and, with Max Born and Pascual Jordan, accomplished the first complete and correct definition of quantum mechanics, through the invention of Matrix mechanics.

While at Chicago, he took a course under the Nobel Prize-winning physicist Robert A. Millikan, which exposed him to the old quantum theory.

While these result in some contradictions and lack completeness in a mathematical sense ( being based on axioms that are " merely " self-evident, but not robust under the stresses of radical scepticism ), the paradoxes can nonetheless be analysed rationally using the subatomic applications of quantum cosmology-particularly through the employment of the Schrödinger wave equations.

While the value of α can be estimated from the values of the constants appearing in any of its definitions, the theory of quantum electrodynamics ( QED ) provides a way to measure α directly using the quantum Hall effect or the anomalous magnetic moment of the electron.

While de Broglie – Bohm theory has Lagrangians and Hamilton-Jacobi equations as a primary focus and backdrop, with the icon of the quantum potential, Bohmian mechanics considers the continuity equation as primary and has the guiding equation as its icon.

While at Berkeley, he was a member of the Fundamental Fysiks Group, founded in May 1975 by Elizabeth Rauscher and George Weissmann, which met weekly to discuss philosophy and quantum physics.

While normal modes are wave-like phenomena in classical mechanics, they have particle-like properties due to the wave – particle duality of quantum mechanics.

While there has been a recent proposal relating to observation of naked singularities, and doubly special relativity, as a part of a program called loop quantum cosmology, as of now there is no experimental observation for which loop quantum gravity makes a prediction not made by the Standard Model or general relativity ( a problem that plagues all current theories of quantum gravity ).

While generally praised for its fast gameplay and unique mechanics, it ultimately failed to gain a very large market presence.

While there have been many variations in overall focus, gameplay and features in MUDs, some distinct sub-groups have formed that can be used to help categorize different game mechanics, game genres and non-game uses.

While he is best known for the Kolmogorov – Arnold – Moser theorem regarding the stability of integrable Hamiltonian systems, he made important contributions in several areas including dynamical systems theory, catastrophe theory, topology, algebraic geometry, classical mechanics and singularity theory, including posing the ADE classification problem, since his first main result — the partial solution of Hilbert's thirteenth problem in 1957 at the age of 19.

While none of the stories has a plot or character connection with the next, a recurring theme is the conflict of the cold mechanics of technology and the psychology of people.

" While Castelnau himself dismissed this claim as " absolutely preposterous ," and the fluid mechanics of such a thing occurring literally defy the laws of physics, it remains one of the more stubborn myths about the candiru.

While the ontology of classical mechanics is part of the ontology of de Broglie – Bohm theory, the dynamics are very different.

While gaits can be classified by footfall, new work involving whole-body kinematics and force-plate records has given rise to an alternative classification scheme, based on the mechanics of the movement.

While these fanciful images feed the misconception, the mechanics of the situation reveal that the Colossus could not have straddled the harbor as described in Lemprière's Classical Dictionary.

While some shorts have the Mickey Mouse Works title card background, others have the House of Mouse version ( the Mouse Works version has various mechanics in the background, including a Mickey shaped one and one with the Mouse Works text inside it, but the House of Mouse version has various moving swirls ) ref > Mickey's Laugh Factory.

While early tactical shooters had simple computer-controlled teammates who offered support fire, the artificial intelligence in later games has evolved with more complex teammate responses such as cover-fire mechanics.

While at École Centrale, Norbert studied physics, mechanics, and engineering.

While the game follows its own story and maps, much of the game utilizes the same game play mechanics, even going as far as adding in a " classic " mode that removed all of the game's graphics, replacing it with a wireframe environment, 8-bit-style sprites for monsters and characters, and chiptune music.

While anti de Sitter space does not correspond to gravity in general relativity with the observed cosmological constant, an anti de Sitter space is believed to correspond to other forces in quantum mechanics ( like electromagnetism, the weak nuclear force and the strong nuclear force ) described via string theory.

While the second law of thermodynamics predicts that the entropy of an isolated system should tend to increase until it reaches equilibrium, it became apparent after the discovery of statistical mechanics that the second law is only a statistical one, suggesting that there should always be some nonzero probability that the entropy of an isolated system might spontaneously decrease ; the fluctuation theorem precisely quantifies this probability.

While cyanobacteria have been traditionally considered algae, recent works usually exclude them due to large differences such as the lack of membrane-bound organelles, the presence of a single circular chromosome, the presence of peptidoglycan in the cell walls, and ribosomes different in size and content from those of the Eukaryotes .< ref >

While initiated in England, competitive men's badminton in Europe has traditionally been dominated by Denmark.

While creating a more feminine figure, male cross-dressers will often utilize different types and styles of breast forms, which are silicone prostheses traditionally used by women who have undergone mastectomies to recreate the visual appearance of a breast.

While this method is traditionally attributed to a 1965 paper by J. W. Cooley and J. W. Tukey, Gauss developed it as a trigonometric interpolation method.

While traditionally couplets rhyme, not all do.

While Britain, Australia and New Zealand have traditionally employed the European usage ( below ), they have been moving to the U. S. system more recently.

While supporters of the merger argued that there would be economies of scale and that the sales of PCs would drive sales of printers and cameras, Walter Hewlett was convinced that PCs were a low-margin but risky business that would not contribute and would likely dilute the old HP's traditionally profitable Imaging and Printing division.

While traditionally accepted as the genuine words of Moses delivered on the eve of the occupation of Canaan, a broad consensus of modern scholars now see its origins in traditions from Israel ( the northern kingdom ) brought south to the Kingdom of Judah in the wake of the Assyrian destruction of Samaria ( 8th century BCE ) and then adapted to a program of nationalist reform in the time of King Josiah ( late 7th century ), with the final form of the modern book emerging in the milieu of the return from the Babylonian exile during the late 6th century.

While ecosystem goods have traditionally been recognized as being the basis for things of economic value, ecosystem services tend to be taken for granted.

While these epistles are traditionally attributed to Paul of Tarsus, there are a few scholars who consider them pseudepigraphical.

While his accession is traditionally dated to 660 BC, no historically firm dates can be assigned to this early emperor's life or reign, nor to the reigns of his early successors.

While Sanskrit has six classes, Latin is traditionally said to have five declension classes, and Ancient Greek three declension classes.

While the gay subculture grew, with official and underground press alike discussing the subject of homosexuality, the traditionally conservative attitudes towards sexuality were used by the secret police to harass and put pressure on individuals.

While the Scottish Enlightenment is traditionally considered to have concluded toward the end of the 18th century, disproportionately large Scottish contributions to British science and letters continued for another 50 years or more, thanks to such figures as the mathematicians and physicists James Clerk Maxwell, Lord Kelvin, and the engineers and inventors James Watt and William Murdoch, whose work was critical to the technological developments of the Industrial Revolution throughout Britain.

While the exact location of the grave is unknown, a stone was added in the 19th century to mark a grave traditionally thought to be Calvin's.

While traditionally most monarchs have been male, female monarchs have also ruled in history ; the term queen regnant refers to a ruling monarch, as distinct from a queen consort, the wife of a reigning king.

While Nomic is traditionally capitalized as the proper name of the game it describes, it has also sometimes been used in a more informal way as a lowercased generic term, nomic, referring to anything with Nomic-like characteristics, including games where the rules may be changed during play as well as non-gaming situations where it can be alleged that " rules lawyers " are tinkering with the process used to amend rules and policies ( in an organization or community ) in a manner akin to a game of Nomic.

While civil law systems have traditionally put great pains in defining the notion of private property, how it may be acquired, transferred, or lost, socialist law systems provide for most property to be owned by the state or by agricultural co-operatives, and having special courts and laws for state enterprises.

While scattered movements and organizations dedicated to women's rights existed previously, the 1848 Seneca Falls Convention in New York is traditionally held as the start of the American women's rights movement.

While traditionally these words have been understood to be either Jewish words whose meaning has been derived from characteristics of these Canaanite deities or references to demons, some interpret these as evidence of Israelite recognition of these gods as part of the military retinue of Yahweh.

While not observed nationally throughout the United States, a number of traditionally ethnic French cities and regions in the country have notable celebrations.

While Australian sparkling Shiraz traditionally have had some sweetness, a number of Australian winemakers also make a full-bodied sparkling dry Shiraz, that contains the complexity and sometimes earthy notes that are normally found in still wine.

While historians have traditionally suggested that his parents sent him to Lake Forest to discourage his interest in jazz, others have begun to doubt this version of events, believing that he may have been sent away in response to his arrest.

While action films have traditionally been a reliable source of revenue for movie studios, relatively few action films garner critical praise, mainly because of their two-dimensional heroes or villains.