* Quantum tic tac toe allows players to place a quantum superposition of numbers on the board, i. e. the players ' moves are " superpositions " of plays in the original classical game.

Quantum mechanics is different, because the numbers can be positive or negative.

Quantum amplitudes give the rate at which amplitudes change in time, and they are mathematically exactly the same except that they are complex numbers.

Quantum numbers often describe specifically the energies of electrons in atoms, but other possibilities include angular momentum, spin, etc.

Quantum mechanically, this corresponds to mixing orbitals that differ in the l and m quantum numbers, such as the s ( l = 0 ) and p ( l = 1 ) atomic orbitals.

Quantum mechanics reduce to classical physics when the quantum numbers are high.

Siteswap ( also called Quantum Juggling by the inventor and Cambridge notation in the United Kingdom ) is a notation used to describe juggling patterns.

Quantum decoherence does not describe the actual process of the wavefunction collapse, but it explains the conversion of the quantum probabilities ( that exhibit interference effects ) to the ordinary classical probabilities.

This does not mean that chemistry is never involved with plasma or nuclear sciences or even bosonic fields nowadays, since areas such as Quantum Chemistry and Nuclear Chemistry are currently well developed and formally recognized sub-fields of study under the Chemical sciences ( Chemistry ), but what is now formally recognized as subject of study under the Chemistry category as a science is always based on the use of concepts that describe or explain phenomena either from matter or to matter in the atomic or molecular scale, including the study of the behavior of many molecules as an aggregate or the study of the effects of a single proton on a single atom, but excluding phenomena that deal with different ( more " exotic ") types of matter ( e. g. Bose-Einstein condensate, Higgs Boson, dark matter, naked singularity, etc.

Quantum mechanics can be used to describe spacetime as being non-empty at extremely small scales, fluctuating and generating particle pairs that appear and disappear incredibly quickly.

EPR tried to set up a paradox to question the range of true application of Quantum Mechanics: Quantum theory predicts that both values cannot be known for a particle, and yet the EPR thought experiment purports to show that they must all have determinate values.

Rather, complementarity means that the composition of physical properties for S ( such as position and momentum both having values within certain ranges ), using propositional connectives, does not obey the rules of classical propositional logic ( see also Quantum logic ).

Quantum mechanics tells us that the total ( kinetic and potential ) energy of the oscillator, E, has a set of discrete values:

Quantum indeterminacy is the assertion that the state of a system does not determine a unique collection of values for all its measurable properties.

* Arthur Wightman: Quantum field theory in terms of vacuum expectation values.

For quantum field theories in which perturbation theory breaks down at low energies ( for example, Quantum chromodynamics or the BCS theory of superconductivity ) field operators may have non-vanishing vacuum expectation values called condensates.

Quantum mechanically, the chiral current is not conserved: Jackiw discovered this due to the non-vanishing of a triangle diagram.

In addition, there have been attempts to construct theories for quantities that are notionally similar to probabilities but do not obey all their rules ; see, for example, Free probability, Fuzzy logic, Possibility theory, Negative probability and Quantum probability.

Quantum field theories involve quantities that when explained to non-experts are commonly described as representing intangible ideas like probabilities and possible paths that a quantum could take to get from one place to another.

Quantum chaos is the field of physics attempting to build a bridge between the theories of quantum mechanics and classical dynamics.

Loop Quantum Gravity has a covariant formulation that provides at present the best formulation of the dynamics of the theory.

The QCD ( Quantum Chromodynamics ) dynamics of the hadronization process are not yet fully understood, but are modeled and parameterized in a number of phenomenological studies, including the Lund string model and in various long-range QCD approximation schemes.

In his book Quantum Theory as an Emergent Phenomenon, published 2004, Adler presented his trace dynamics, a framework in which quantum field theory emerges from a matrix theory.

* Quantum brain dynamics

*" Quantum dynamics of single trapped ions " D Leibfried, R Blatt, C Monroe, D Wineland.

* Quantum annealing, a method for finding solutions to combinatorial optimisation problems and ground states of glassy systems using quantum fluctuations

According to a poll at a Quantum Mechanics workshop in 1997 ,< ref > the Copenhagen interpretation is the most widely-accepted specific interpretation of quantum mechanics, followed by the many-worlds interpretation.

The books that were influential in the early development of computational quantum chemistry include Linus Pauling and E. Bright Wilson's 1935 Introduction to Quantum Mechanics – with Applications to Chemistry, Eyring, Walter and Kimball's 1944 Quantum Chemistry, Heitler's 1945 Elementary Wave Mechanics – with Applications to Quantum Chemistry, and later Coulson's 1952 textbook Valence, each of which served as primary references for chemists in the decades to follow.

The idea of MWI originated in Everett's Princeton Ph. D. thesis " The Theory of the Universal Wavefunction ", developed under his thesis advisor John Archibald Wheeler, a shorter summary of which was published in 1957 entitled " Relative State Formulation of Quantum Mechanics " ( Wheeler contributed the title " relative state "; Everett originally called his approach the " Correlation Interpretation ", where " correlation " refers to quantum entanglement ).

Quantum theory and quantum mechanics do not provide single measurement outcomes in a deterministic way.

Bernard d ' Espagnat a French theoretical physicist best known for his work on the nature of reality wrote a paper titled The Quantum Theory and Reality according to the paper: " The doctrine that the world is made up of objects whose existence is independent of human consciousness turns out to be in conflict with quantum mechanics and with facts established by experiment.

* Quantum mass manifests itself as a difference between an object ’ s quantum frequency and its wave number.

Quantum field theory has driven the development of more sophisticated formulations of quantum mechanics, of which the one presented here is a simple special case.

* Quantum logic formulation of quantum mechanics

Quantum dots ( nanoparticles with quantum confinement properties, such as size-tunable light emission ), when used in conjunction with MRI ( magnetic resonance imaging ), can produce exceptional images of tumor sites.

Quantum optics deals with the application of quantum mechanics to optical systems.

* Quantum oscillator may refer to an optical local oscillator, as well as to a usual model in quantum optics.

* Quantum mechanics: In quantum mechanics, which deals with the behavior of very small objects, it is not possible to observe a system without changing the system, and the " observer " must be considered part of the system being observed.

Quantum chemistry, a subfield of physical chemistry especially concerned with the application of quantum mechanics to chemical problems, provides tools to determine how strong and what shape bonds are, how nuclei move, and how light can be absorbed or emitted by a chemical compound.

Quantum mechanics ( QM – also known as quantum physics, or quantum theory ) is a branch of physics dealing with physical phenomena at microscopic scales, where the action is on the order of the Planck constant.

Quantum mechanics departs from classical mechanics primarily at the quantum realm of atomic and subatomic length scales.

Quantum mechanics has since branched out into almost every aspect of 20th century physics and other disciplines, such as quantum chemistry, quantum electronics, quantum optics, and quantum information science.

Quantum coherence is an essential difference between classical and quantum theories, and is illustrated by the Einstein-Podolsky-Rosen paradox.

Quantum coherence is not typically evident at macroscopic scales-although an exception to this rule can occur at extremely low temperatures ( i. e. approaching absolute zero ), when quantum behavior can manifest itself on more macroscopic scales ( see macroscopic quantum phenomena, Bose-Einstein condensate, and Quantum machine ).