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 quantum mechanics traditionally described the world of the very small, it is also needed to explain certain recently investigated macroscopic systems such as superconductors and superfluids.

* 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 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 the improvements are attributed primarily to changes in the brain and not just the hip and / or ankle joints, it is still unknown whether the improvements are due to adaptations in the cerebellum or compensation by other areas of the brain.

While the earlier settlers were primarily of British ancestry, the newer settlers also consisted of Germans, Irish, and African-Americans.

While there are some similarities between the two movements, Theodism derived its origins primarily as a reaction to Wicca.

While the Reno Air Races keep this tradition alive, most air shows today primarily feature a series of aerial demos of short duration.

< p > While the alcohol content of flavored malt beverages is similar to that of most traditional malt beverages, the alcohol in many of them is derived primarily from the distilled spirits component of the added flavors rather than from fermentation .</ p > ( 70 Fed.

While TMV is capable of infecting many plant families these are primarily herbaceous dicots.

While people may gain celebrity status as a result of a successful career in a particular field ( primarily in the areas pertaining towards sports and entertainment ), in other cases, people become celebrities due to media attention for their extravagant lifestyle or wealth ( as in the case of a socialite ); for their connection to a famous person ( as in the case of a relative of a famous person ); or even for their misdeeds ( as in the case of a well-known criminal ).

While primarily utilised for ceremonial purposes, the regiment can be deployed for internal security or police roles if required.

While the Amorphs have the ability to move fast, quietly, and sprout appendages at will, they excel at ' closer-than-melee-range combat, primarily " meme-toxins " against other Amorphs.

Silvermintz notes that, " Historians of economic thought credit Plato, primarily on account of arguments advanced in his Republic, as an early proponent of the division of labor .” Notwithstanding this, Silvermintz argues that, " While Plato recognizes both the economic and political benefits of the division of labor, he ultimately critiques this form of economic arrangement insofar as it hinders the individual from ordering his own soul by cultivating acquisitive motives over prudence and reason.

While the conservative wing of the German political spectrum, primarily formed of the CDU and CSU, enjoys considerable support, this support tends to be less extended to Stoiber.

While primarily written in C ++, Python bindings are also available.

While male versions of the chest protector are also available, they were, until recently, primarily worn by instructors, who are hit far more often during training than their students.

While fascism opposes domestic class conflict, fascism believes that bourgeois-proletarian conflict primarily exists in national conflict between proletarian nations versus bourgeois nations.

While faith in Buddhism does not imply " blind faith ", Buddhist faith nevertheless requires a degree of faith and belief, primarily in the spiritual attainment of Gautama Buddha.

While the first three truths are primarily concerned with understanding the nature of dukkha ( suffering, anxiety, stress ) and its causes, the fourth truth presents a practical method for overcoming dukkha.

While most of the Centers are located around the Washington, D. C., area as part of the Headquarters divisions, two offices – the Office of Regulatory Affairs ( ORA ) and the Office of Criminal Investigations ( OCI ) – are primarily field offices with a workforce spread across the country.

While fused quartz ( primarily composed of SiO < sub > 2 </ sub >) is used for some special applications, it is not very common due to its high glass transition temperature of over 1200 ° C ( 2192 ° F ).< ref > Normally, other substances are added to simplify processing.

While current field hockey appeared in the mid-18th century in England, primarily in schools, it was not until the first half of the 19th century that it became firmly established.

While the ancient Egyptian beliefs usually recognized many gods, worship was often focused primarily upon a supreme deity, and this focus also changed from time to time.

While IGF-2 may be primarily fetal in action it is also essential for development and function of organs such as the brain, liver and kidney.

While most Indian engineering colleges barring IITs emphasize on undergraduate teaching, Jadavpur University is primarily recognized on research, after IITs it has been ranked sixth in research output in India for its engineering faculty.

While most asteroids are composed primarily of rock and metal, Kuiper belt objects are composed largely of frozen volatiles ( termed " ices "), such as methane, ammonia and water.

While they focused primarily on more traditional mission architectures, Zubrin began to collaborate with colleague David Baker on an extremely simple, stripped-down and robust strategy.