In physics,<unk>  is the study of the relationship between energy quanta (radiation) and matter, in particular that between valence shell electrons and photons.<unk>  is a fundamental branch of physics with wide applications in both experimental and theoretical physics.<unk>  theory generalizes all classical theories, including<unk> , electromagnetism (except general relativity), and provides accurate descriptions for many previously unexplained phenomena such as black body radiation and stable electron orbits.The effects of<unk>  are typically not observable on macroscopic scales, but become evident at the atomic and subatomic level.
The word<unk> ” (Latin, “how much”) in<unk>  refers to a discrete unit that<unk>  theory assigns to certain physical quantities, such as the energy of an atom at rest (see Figure 1, at right). The discovery that waves have discrete energy packets (called quanta) that behave in a manner similar to particles led to the branch of physics that deals with atomic and subatomic systems which we today call<unk> . It is the underlying mathematical framework of many fields of physics and chemistry, including condensed matter physics, solid-state physics, atomic physics, molecular physics, computational chemistry,<unk>  chemistry, particle physics, and nuclear physics. The foundations of<unk>  were established during the first half of the twentieth century by Albert Einstein, Werner Heisenberg, Max Planck, Louis de Broglie, Niels Bohr, Erwin Schrödinger, Max Born, John von Neumann, Paul Dirac, Wolfgang Pauli and others. Some fundamental aspects of the theory are still actively studied.
It is currently necessary to use<unk>  to understand the behavior of systems at atomic length scales and smaller. For example, if Newtonian<unk>  governed the workings of an atom, electrons would rapidly travel towards and collide with the nucleus. However, in the natural world the electrons normally remain in an unknown orbital path around the nucleus, defying classical electromagnetism.<unk>  was initially developed to provide a better explanation of the atom, especially the spectra of light emitted by different atomic species. The<unk>  theory of the atom developed as an explanation for the electron's staying in its orbital, which could not be explained by Newton's laws of motion and by Maxwell's laws of classical electromagnetism.
In the formalism of<unk> , the state of a system at a given time is described by a complex wave function (sometimes referred to as orbitals in the case of atomic electrons), and more generally, elements of a complex vector space. This abstract mathematical object allows for the calculation of probabilities of outcomes of concrete experiments. For example, it allows one to compute the probability of finding an electron in a particular region around the nucleus at a particular time. Contrary to classical<unk> , one can never make simultaneous predictions of conjugate variables, such as position and momentum, with arbitrary accuracy. For instance, electrons may be considered to be located somewhere within a region of space, but with their exact positions being unknown. Contours of constant probability, often referred to as “clouds” may be drawn around the nucleus of an atom to conceptualize where the electron might be located with the most probability. It should be stressed that the electron itself is not spread out over such cloud regions. It is either in a particular region of space, or it is not [citation needed]. Heisenberg's uncertainty principle quantifies the inability to precisely locate the particle.
The other exemplar that led to<unk>  was the study of electromagnetic waves such as light. When it was found in 1900 by Max Planck that the energy of waves could be described as consisting of small packets or quanta, Albert Einstein exploited this idea to show that an electromagnetic wave such as light could be described by a particle called the photon with a discrete energy dependent on its frequency. This led to a theory of unity between subatomic particles and electromagnetic waves called wave–particle duality in which particles and waves were neither one nor the other, but had certain properties of both. While<unk>  describes the world of the very small, it also is needed to explain certain “macroscopic<unk>  systems” such as superconductors and superfluids.
Broadly speaking,<unk>  incorporates four classes of phenomena that classical physics cannot account for: (i) the quantization (discretization) of certain physical quantities, (ii) wave-particle duality, (iii) the uncertainty principle, and (iv)<unk>  entanglement. Each of these phenomena is described in detail in subsequent sections.
Quantum mechanics
Chemical symbol
Subscript
Measurement
Theoretical plate
Molecular orbital
Systems biology
Cognitive science