**Atomic electron transition** is a change of an electron from one energy level to another within an atom^{[1]} or artificial atom.^{[2]} It appears discontinuous as the electron "jumps" from one energy level to another, typically in a few nanoseconds or less. It is also known as an **atomic transition or a** **quantum jump**.

Electron transitions cause the emission or absorption of electromagnetic radiation in the form of quantized units called photons. Their statistics are Poissonian, and the time between jumps is exponentially distributed.^{[3]} The damping time constant (which ranges from nanoseconds to a few seconds) relates to the natural, pressure, and field broadening of spectral lines. The larger the energy separation of the states between which the electron jumps, the shorter the wavelength of the photon emitted.

The observability of quantum jumps was predicted by Hans Dehmelt in 1975, and they were first observed using trapped ions of mercury at NIST in 1986.^{[4]}

- Burst noise
- Ensemble interpretation
- Fluorescence
- Glowing pickle demonstration
- Molecular electronic transition for molecules
- Phosphorescence
- Spontaneous emission
- Stimulated emission

**^**Schombert, James. "Quantum physics" University of Oregon Department of Physics**^**Vijay, R; Slichter, D. H; Siddiqi, I (2011). "Observation of Quantum Jumps in a Superconducting Artificial Atom".*Physical Review Letters*.**106**(11): 110502. arXiv:1009.2969. Bibcode:2011PhRvL.106k0502V. doi:10.1103/PhysRevLett.106.110502. PMID 21469850.**^**Observing the quantum jumps of light**^**Itano, W. M.; Bergquist, J. C.; Wineland, D. J. (2015). "Early observations of macroscopic quantum jumps in single atoms" (PDF).*International Journal of Mass Spectrometry*.**377**: 403. Bibcode:2015IJMSp.377..403I. doi:10.1016/j.ijms.2014.07.005.

- Schrödinger, Erwin (August 1952). "Are there quantum jumps? Part I" (PDF).
*The British Journal for the Philosophy of Science*.**3**(10): 109–123. doi:10.1093/bjps/iii.10.109. Part 2 - "There are no quantum jumps, nor are there particles!" by H. D. Zeh,
*Physics Letters***A172**, 189 (1993). - Gleick, James (October 21, 1986). "Physicists Finally Get To See the Quantum Jump".
*The New York Times*. Retrieved 2013-08-23.

Antihydrogen (H) is the antimatter counterpart of hydrogen. Whereas the common hydrogen atom is composed of an electron and proton, the antihydrogen atom is made up of a positron and antiproton. Scientists hope studying antihydrogen may shed light on the question of why there is more matter than antimatter in the observable universe, known as the baryon asymmetry problem. Antihydrogen is produced artificially in particle accelerators. In 1999, NASA gave a cost estimate of $62.5 trillion per gram of antihydrogen (equivalent to $94 trillion today), making it the most expensive material to produce. This is due to the extremely low yield per experiment, and high opportunity cost of using a particle accelerator.

Bloch sphereIn quantum mechanics, the **Bloch sphere** is a geometrical representation of the pure state space of a two-level quantum mechanical system (qubit), named after the physicist Felix Bloch.

Quantum mechanics is mathematically formulated in Hilbert space or projective Hilbert space.
The space of pure states of a quantum system is given by the one-dimensional subspaces of the corresponding Hilbert space (or the "points" of the projective Hilbert space).
For a two-dimensional Hilbert space, this is simply the complex projective line ℂℙ^{1}. This is the Bloch sphere.

The Bloch sphere is a unit 2-sphere, with antipodal points corresponding to a pair of mutually orthogonal state vectors.
The north and south poles of the Bloch sphere are typically chosen to correspond to the standard basis vectors and , respectively,
which in turn might correspond e.g. to the spin-up and spin-down states of an electron.
This choice is arbitrary, however.
The points on the surface of the sphere correspond to the pure states of the system, whereas the interior points correspond to the mixed states.
The Bloch sphere may be generalized to an *n*-level quantum system, but then the visualization is less useful.

For historical reasons, in optics the Bloch sphere is also known as the Poincaré sphere and specifically represents different types of polarizations. Six common polarization types exist and are called Jones Vectors. Indeed Henri Poincaré was the first to suggest the use of this kind of geometrical representation at the end of 19th century, as a three-dimensional representation of Stokes parameters.

The natural metric on the Bloch sphere is the Fubini–Study metric. The mapping from the unit 3-sphere in the two-dimensional state space ℂ^{2} to the Bloch sphere is the Hopf fibration, with each ray of spinors mapping to one point on the Bloch sphere.

Burst noise is a type of electronic noise that occurs in semiconductors and ultra-thin gate oxide films. It is also called random telegraph noise (RTN), popcorn noise, impulse noise, bi-stable noise, or random telegraph signal (RTS) noise.

It consists of sudden step-like transitions between two or more discrete voltage or current levels, as high as several hundred microvolts, at random and unpredictable times. Each shift in offset voltage or current often lasts from several milliseconds to seconds, and sounds like popcorn popping if hooked up to an audio speaker.Popcorn noise was first observed in early point contact diodes, then re-discovered during the commercialization of one of the first semiconductor op-amps; the 709. No single source of popcorn noise is theorized to explain all occurrences, however the most commonly invoked cause is the random trapping and release of charge carriers at thin film interfaces or at defect sites in bulk semiconductor crystal. In cases where these charges have a significant impact on transistor performance (such as under an MOS gate or in a bipolar base region), the output signal can be substantial. These defects can be caused by manufacturing processes, such as heavy ion implantation, or by unintentional side-effects such as surface contamination.Individual op-amps can be screened for popcorn noise with peak detector circuits, to minimize the amount of noise in a specific application.Burst noise is modeled mathematically by means of the telegraph process, a Markovian continuous-time stochastic process that jumps discontinuously between two distinct values.

DayA day, a unit of time, is approximately the period of time during which the Earth completes one rotation around its axis with respect to the Sun (solar day). In 1960, the second was redefined in terms of the orbital motion of the Earth in year 1900, and was designated the SI base unit of time. The unit of measurement "day", was redefined as 86 400 SI seconds and symbolized d. In 1967, the second and so the day were redefined by atomic electron transition. A civil day is usually 86 400 seconds, plus or minus a possible leap second in Coordinated Universal Time (UTC), and occasionally plus or minus an hour in those locations that change from or to daylight saving time.

Day can be defined as each of the twenty-four-hour periods, reckoned from one midnight to the next, into which a week, month, or year is divided, and corresponding to a rotation of the earth on its axis. However its use depends on its context, for example when people say 'day and night', 'day' will have a different meaning. It will mean the interval of light between two successive nights; the time between sunrise and sunset. People tend to sleep during the night and are awake at a day, in this instance 'day' will mean time of light between one night and the next. However, in order to be clear when using 'day' in that sense, "daytime" should be used to distinguish it from "day" referring to a 24-hour period; this is since daytime usually always means 'the time of the day between sunrise and sunset. The word day may also refer to a day of the week or to a calendar date, as in answer to the question, "On which day?" The life patterns (circadian rhythms) of humans and many other species are related to Earth's solar day and the day-night cycle.

Density matrixA density matrix is a matrix that describes the statistical state of a system in quantum mechanics. The density matrix is especially helpful for dealing with mixed states, which consist of a statistical ensemble of several different quantum systems. The opposite of a mixed state is a pure state. State vectors, also called kets, describe only pure states, whereas a density matrix can describe both pure and mixed states.

Describing a quantum state by its density matrix is a fully general alternative formalism to describing a quantum state by its ket (state vector) or by its statistical ensemble of kets. However, in practice, it is often most convenient to use density matrices for calculations involving mixed states, and to use kets for calculations involving only pure states.

The density matrix is the quantum-mechanical analogue to a phase-space probability measure (probability distribution of position and momentum) in classical statistical mechanics.

Mixed states arise in situations where the experimenter does not know which particular states are being manipulated. Examples include a system in thermal equilibrium at a temperature above absolute zero, or a system with an uncertain or randomly varying preparation history (so one does not know which pure state the system is in). Also, if a quantum system has two or more subsystems that are entangled, then each subsystem must be treated as a mixed state even if the complete system is in a pure state. The density matrix is also a crucial tool in quantum decoherence theory.

The density matrix is a representation of a linear operator called the density operator. The density matrix is obtained from the density operator by choice of basis in the underlying space. In practice, the terms density matrix and density operator are often used interchangeably. Both matrix and operator are self-adjoint (or Hermitian), positive semi-definite, of trace one, and may

be infinite-dimensional.

Ensemble interpretationThe ensemble interpretation of quantum mechanics considers the quantum state description to apply only to an ensemble of similarly prepared systems, rather than supposing that it exhaustively represents an individual physical system.The advocates of the ensemble interpretation of quantum mechanics claim that it is minimalist, making the fewest physical assumptions about the meaning of the standard mathematical formalism. It proposes to take to the fullest extent the statistical interpretation of Max Born, for which he won the Nobel Prize in Physics. For example, a new version of the ensemble interpretation that relies on a new formulation of probability theory was introduced by Raed Shaiia, which showed that the laws of quantum mechanics are the inevitable result of this new formulation. On the face of it, the ensemble interpretation might appear to contradict the doctrine proposed by Niels Bohr, that the wave function describes an individual system or particle, not an ensemble, though he accepted Born's statistical interpretation of quantum mechanics. It is not quite clear exactly what kind of ensemble Bohr intended to exclude, since he did not describe probability in terms of ensembles. The ensemble interpretation is sometimes, especially by its proponents, called "the statistical interpretation", but it seems perhaps different from Born's statistical interpretation.

As is the case for "the" Copenhagen interpretation, "the" ensemble interpretation might not be uniquely defined. In one view, the ensemble interpretation may be defined as that advocated by Leslie E. Ballentine, Professor at Simon Fraser University. His interpretation does not attempt to justify, or otherwise derive, or explain quantum mechanics from any deterministic process, or make any other statement about the real nature of quantum phenomena; it intends simply to interpret the wave function. It does not propose to lead to actual results that differ from orthodox interpretations. It makes the statistical operator primary in reading the wave function, deriving the notion of a pure state from that. In the opinion of Ballentine, perhaps the most notable supporter of such an interpretation was Albert Einstein:

The attempt to conceive the quantum-theoretical description as the complete description of the individual systems leads to unnatural theoretical interpretations, which become immediately unnecessary if one accepts the interpretation that the description refers to ensembles of systems and not to individual systems.

Nevertheless, one may doubt as to whether Einstein, over the years, had in mind one definite kind of ensemble.

History of subatomic physicsThe idea that matter consists of smaller particles and that there exists a limited number of sorts of primary, smallest particles in nature has existed in natural philosophy at least since the 6th century BC. Such ideas gained physical credibility beginning in the 19th century, but the concept of "elementary particle" underwent some changes in its meaning: notably, modern physics no longer deems elementary particles indestructible. Even elementary particles can decay or collide destructively; they can cease to exist and create (other) particles in result.

Increasingly small particles have been discovered and researched: they include molecules, which are constructed of atoms, that in turn consist of subatomic particles, namely atomic nuclei and electrons. Many more types of subatomic particles have been found. Most such particles (but not electrons) were eventually found to be composed of even smaller particles such as quarks. Particle physics studies these smallest particles and their behaviour under high energies, whereas nuclear physics studies atomic nuclei and their (immediate) constituents: protons and neutrons.

Index of physics articles (A)The index of physics articles is split into multiple pages due to its size.

To navigate by individual letter use the table of contents below.

Maxwell–Bloch equationsThe Maxwell–Bloch equations, also called the optical Bloch equations, were first derived by Tito Arecchi and Rodolfo Bonifacio of Milan, Italy. They describe the dynamics of a two-state quantum system interacting with the electromagnetic mode of an optical resonator. They are analogous to (but not at all equivalent to) the Bloch equations which describe the motion of the nuclear magnetic moment in an electromagnetic field. The equations can be derived either semiclassically or with the field fully quantized when certain approximations are made.

Molecular electronic transitionMolecular electronic transitions take place when electrons in a molecule are excited from one energy level to a higher energy level. The energy change associated with this transition provides information on the structure of a molecule and determines many molecular properties such as colour. The relationship between the energy involved in the electronic transition and the frequency of radiation is given by Planck's relation.

Quantum jumpQuantum jump may refer to:

Atomic electron transition or a similar transition between quantum states, which is a scientific phenomenon

Quantum Jump, a British rock music band

Quantum jump method, a technique in computational physics

Quantum leap (disambiguation)A quantum leap is an atomic electron transition between quantum states.

Quantum leap may also refer to:

Quantum Leap, a television series

An abrupt, extreme change or paradigm shift

A sub-brand produced by the educational toy company LeapFrog.

Quantum stateIn quantum physics, **quantum state** refers to the state of an isolated quantum system. A quantum state provides a probability distribution for the value of each observable, i.e. for the outcome of each possible measurement on the system. Knowledge of the quantum state together with the rules^{[clarification needed]} for the system's evolution in time exhausts all that can be predicted about the system's behavior.

A mixture of quantum states is again a quantum state. Quantum states that cannot be written as a mixture of other states are called **pure quantum states**, all other states are called **mixed quantum states**.

Mathematically, a **pure quantum state** can be represented by a ray in a Hilbert space over the complex numbers. The ray is a set of nonzero vectors differing by just a complex scalar factor; any of them can be chosen as a **state vector** to represent the ray and thus the state. A unit vector is usually picked, but its phase factor can be chosen freely anyway. Nevertheless, such factors are important when state vectors are added together to form a superposition.

Hilbert space is a generalization of the ordinary Euclidean space and it contains all possible pure quantum states of the given system^{[citation needed]}. If this Hilbert space, by choice of representation (essentially a choice of basis corresponding to a complete set of observables), is exhibited as a function space (a Hilbert space in its own right), then the representatives^{[clarification needed]} are called wave functions.

For example, when dealing with the energy spectrum of the electron in a hydrogen atom, the relevant state vectors are identified by the principal quantum number *n*, the angular momentum quantum number *l*, the magnetic quantum number *m*, and the spin z-component *s*_{z}^{[citation needed]}. A more complicated case is given (in bra–ket notation) by the spin part of a state vector^{[clarification needed]}.

which involves superposition of joint spin states for two particles with spin ^{1}⁄_{2}^{[clarification needed]}.

A **mixed quantum state** corresponds to a probabilistic mixture of pure states^{[why?]}; however, different distributions of pure states can generate equivalent (i.e., physically indistinguishable) mixed states. Mixed states are described by so-called density matrices. A pure state can also be recast as a density matrix; in this way, pure states can be represented as a subset of the more general mixed states.

For example, if the spin of an electron is measured in any direction, e.g. with a Stern–Gerlach experiment, there are two possible results: up or down. The Hilbert space for the electron's spin is therefore two-dimensional. A pure state here is represented by a two-dimensional complex vector , with a length of one; that is, with

where and are the absolute values of and . A mixed state, in this case, has the structure of a matrix that is Hermitian, positive-definite, and has trace 1.

Before a particular measurement is performed on a quantum system, the theory usually gives only a probability distribution for the outcome, and the form that this distribution takes is completely determined by the quantum state and the observable describing the measurement. These probability distributions arise for both mixed states and pure states: it is impossible in quantum mechanics (unlike classical mechanics) to prepare a state in which all properties of the system are fixed and certain. This is exemplified by the uncertainty principle, and reflects a core difference between classical and quantum physics. Even in quantum theory, however, for every observable there are some states that have an exact and determined value for that observable.

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