* 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 describe values of conserved quantities in the dynamics of the quantum system.

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.

Quantum nonlocality is often proposed as a mechanism for superluminal communication.

Quantum optics often connotes fundamental research, whereas photonics is used to connote applied research and development.

Einstein often referred to the " inner voice " as a source of both moral and physical knowledge: " Quantum mechanics is very impressive.

Courses are generally given within a department, and often named for the department, e. g. Physics 230: Quantum mechanics.

In the case of a Tonks – Girardeau gas ( TG ), so many properties of this one-dimensional string of bosons would be sufficiently fermion-like that the situation is often referred to as the ' fermionization ' of bosons. Tonks – Girardeau gas coincide with quantum Nonlinear Schrödinger equation for infinite repulsion, which can be efficiently analyzed by Quantum inverse scattering method.

Quantum mechanical departures from classical physics are most often encountered at small length scales, very low or very high energies, or low temperatures.

He has lectured on subjects related to quantum physics and consciousness since the 1960s, often under the name Dr. Quantum or Captain Quantum.

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.

Quasar's powers are derived from the pair of Quantum Bands fused to his wrists ( or more specifically, from the seven gems on each of the bands ).

Quantum mechanics can also provide quantitative insight into ionic and covalent bonding processes by explicitly showing which molecules are energetically favorable to which others, and the magnitudes of the energies involved.

An example of this is the beta function for Quantum Chromodynamics ( QCD ), and as a result the QCD coupling decreases at high energies.

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.

As a result, he also can access the Quantum Field and use its energies for a variety of powers.

The mathematical definition is simple ( and analogous to the so-called Wilson loop in Quantum chromodynamics ): One considers for example expressions (" total energies " or " Hamiltonians ") of the form

Quantum mechanics is a set of principles describing physical reality at the atomic level of matter ( molecules and atoms ) and the subatomic ( electrons, protons, and even smaller particles ).

Quantum tunneling is vital to the operation of many devices-even in the simple light switch, as otherwise the electrons in the electric current could not penetrate the potential barrier made up of a layer of oxide.

Quantum theory also provides accurate descriptions for many previously unexplained phenomena, such as black body radiation and the stability of the orbitals of electrons in atoms.

Quantum entanglement occurs when particles such as photons, electrons, molecules as large as buckyballs ,< ref > Nature: Wave – particle duality of C < sub > 60 </ sub > molecules, 14 October 1999.

Carver Mead's Collective Electrodynamics: Quantum Foundations of Electromagnetism ( 2000 ) analyzes the behavior of electrons and photons purely in terms of electron wave functions, and attributes the apparent particle-like behavior to quantization effects and eigenstates.

Quantum mechanics states that electrons in an atom cannot take on any arbitrary energy value.

Quantum mechanically it is not unreasonable to assume that the momenta of the electrons and nuclei in a molecule are comparable in magnitude ( recall that the corresponding operators do not contain mass and think of the molecule as a box containing the electrons and nuclei and see particle in a box ).

Quantum tunneling and quantum entanglement are interesting areas involving electrons ( or photons ).

Quantum theory states that orbiting electrons of an atom must occupy discrete energy levels in order to be stable.

* Quantum wires, which confine electrons or holes in two spatial dimensions and allow free propagation in the third.

* Quantum wells, which confine electrons or holes in one dimension and allow free propagation in two dimensions.

* electrons moving along edge states in the fractional Quantum Hall Effect

Quantum orbital motion involves the quantum mechanical motion of rigid particles ( such as electrons ) about some other mass, or about themselves.

Quantum electronics is the area of physics dealing with the effects of quantum mechanics on the behaviour of electrons in matter.

Quantum mechanics was developed with the aim of describing atoms and explaining the observed spectral lines in a measurement apparatus.

Quantum mechanics is also critically important for understanding how individual atoms combine covalently to form molecules.

* Chemistry: Molecular theory — Kinetic theory of gases — Molecular orbital theory — Valence bond theory — Transition state theory — RRKM theory — Chemical graph theory — Flory-Huggins solution theory — Marcus theory — Lewis theory ( successor to Brønsted – Lowry acid – base theory ) — HSAB theory — Debye – Hückel theory — Thermodynamic theory of polymer elasticity — Reptation theory — Polymer field theory — Møller – Plesset perturbation theory — Density Functional Theory — Frontier molecular orbital theory — Polyhedral skeletal electron pair theory — Baeyer strain theory — Quantum theory of atoms in molecules — Collision theory — Ligand field theory ( successor to Crystal field theory ) — Variational Transition State Theory — Benson group increment theory — Specific ion interaction theory

Quantum mechanics predicts that certain physical phenomena, such as the nuclear decay of atoms, are fundamentally random and cannot, in principle, be predicted ( for a discussion of empirical verification of quantum unpredictability, see Bell test experiments.

With chapters like " The first encounter with the science about atoms ", " Quantum mechanics and talks with Einstein ", " Talk about the relation between biology, physics and chemistry " or " Talks about language " and " The behavior of an individual

: Quantum physics holds that certain events such as radioactive decay and movement of particles are completely random when taken at the level of single atoms or smaller.

When the Bohr treatment is extended to hydrogenic-like atoms using the Quantum Rule, the Bohr radius becomes

Quantum mechanics provides equations based on the Hartree-Fock method and the Roothaan equations that CNDO uses to model atoms and their locations.

His work on atoms in molecules is the subject of his book, Atoms in Molecules: A Quantum Theory.