Quantum mechanics Quantum mechanics In quantum mechanics, an adiabatic process is an infinitely slow change in the Hamiltonian of a system. Adiabatic processes are important idealizations of "sufficiently slow" processes and bear important consequences for quantum mechanics (see adiabatic theorem). ...more on Wikipedia about "Adiabatic process (quantum mechanics)"
The adiabatic theorem is an important theorem in quantum mechanics which provides the foundation for perturbative quantum field theory. ...more on Wikipedia about "Adiabatic theorem"
The Aharonov-Bohm effect, sometimes called the Ehrenberg-Siday-Aharonov-Bohm effect, is a quantum mechanical phenomenon by which a charged particle is affected by electromagnetic fields in regions from which the particle is excluded. The earliest form of this effect was predicted by Werner Ehrenberg and R.E. Siday in 1949, and similar effects were later rediscovered by Aharonov and Bohm in 1959. Such effects are predicted to arise from both magnetic fields and electric fields, but the magnetic version has been easier to observe. In general, the profound consequence of Aharonov-Bohm effects is that knowledge of the classical electromagnetic field acting locally on a particle is not sufficient to predict its quantum-mechanical behavior. ...more on Wikipedia about "Aharonov-Bohm effect"
In quantum mechanics, angular momentum is defined like momentum - not as a quantity but as an operator on the wave function: ...more on Wikipedia about "Angular momentum operator"
In quantum mechanics, Bargmann's limit, named for Valentine Bargmann, provides an upper bound on the number Nl of bound states in a system. It takes the form ...more on Wikipedia about "Bargmann's limit"
Quantum mechanics is a physical science dealing with the behaviour of matter and electromagnetic waves on the scale of atoms and subatomic particles. It also forms the basis for the contemporary understanding of how large objects such as stars and galaxies, and cosmological events such as the Big Bang, can be analyzed and explained. Its success is due to its accurate prediction of the physical behaviour of systems, including systems where Newtonian mechanics fails. This is most often observed in systems at the atomic scale or smaller, or at very low or very high energies, or at extremely low temperatures. Quantum mechanics is the basis of modern developments in chemistry, molecular biology, and electronics, and the foundation for the technology that has transformed the world in the last fifty years. ...more on Wikipedia about "Basics of quantum mechanics"
In quantum mechanics, the Berry phase is a phase acquired by quantum states when subjected to adiabatic processes, resulting from the geometrical properties of the parameter space of the Hamiltonian. It was named after Sir Michael Berry, and is also known as Pancharatnam-Berry or geometric phase. It appears in particular in the theory of the Aharonov-Bohm effect and of the conical intersection of potential energy surfaces. In the case of the Aharonov-Bohm effect, the adiabatic parameter is the magnetic field inside the solenoid. In the case of the conical intersection, the adiabatic parameters are the molecular coordinates. Apart from quantum mechanics, it arises in a variety of other wave systems, such as classical optics. Generally speaking, it occurs whenever one can externally control at least two parameters affecting a wave. ...more on Wikipedia about "Berry phase"
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In quantum mechanics, the Born probability is a probability of an event calculated from a wavefunction or more generally from the density matrix. The probability (or its density) equals the squared modulus of the complex amplitude : ...more on Wikipedia about "Born probability"
An ideal Bose gas is a quantum-mechanical version of a classical ideal gas. It is composed of bosons, which have an integral value of spin, and obey Bose-Einstein statistics. The statistical mechanics of bosons were developed by Satyendra Nath Bose for photons, and extended to massive particles by Albert Einstein who realized that an ideal gas of bosons would form a condensate at a low enough temperature, unlike a classical ideal gas. This condensate is known as a Bose-Einstein condensate. ...more on Wikipedia about "Bose gas"
A Bose-Einstein condensate is a phase of matter formed by bosons cooled to temperatures very near to absolute zero. The first such condensate was produced by Eric Cornell and Carl Wieman in 1995 at the University of Colorado at Boulder, using a gas of rubidium atoms cooled to 170 nanokelvins (nK). Under such conditions, a large fraction of the atoms collapse into the lowest quantum state. ...more on Wikipedia about "Bose-Einstein condensate"
(Bose-Einstein statistics) :For other topics related to Einstein see Einstein (disambiguation). ...more on Wikipedia about "Bose-Einstein statistics"
In physics, a bound state is a composite of two or more building blocks ( particles or bodies) that behaves as a single object. In quantum mechanics (where the number of particles is conserved), a bound state is a state in the Hilbert space that corresponds to two or more particles whose interaction energy is negative, and therefore these particles cannot be separated unless energy is spent. The energy spectrum of a bound state is discrete, unlike the continuous spectrum of isolated particles. (Actually, it is possible to have unstable bound states with a positive interaction energy provided that there is a "energy barrier" that has to be tunnelled through in order to decay. This is true for some radioactive nuclei.) ...more on Wikipedia about "Bound state"
The Breit equation is a relativistic wave equation derived by Gregory Breit in 1929 based on the Dirac equation, which formally describes two or more massive spin-1/2 particles ( electrons, for example) interacting electromagnetically to the first order in perturbation theory. It accounts for magnetic interactions and retardation effects to the order of 1/c2. When other quantum electrodynamic effects are negligible, this equation has been shown to give results in good agreement with experiment. ...more on Wikipedia about "Breit equation"
In physics, C parity or charge parity is a multiplicative quantum number of some particles that describes its behavior under a symmetry operation of charge conjugation (see C-symmetry). ...more on Wikipedia about "C parity"
In physics, the canonical commutation relation is the relation ...more on Wikipedia about "Canonical commutation relation"
Canonical conjugate variables in physics are pairs of variables that share an uncertainty relation. The terminology comes from Hamiltonian mechanics. ...more on Wikipedia about "Canonical conjugate variables"
The classical limit is the ability of a physical theory to approximate or "recover" classical mechanics when considered over special values of its parameters. The classical limit is used with physical theories that predict non-classical behavior. A postulate called the correspondence principle was introduced to quantum theory by Niels Bohr; it states that, in effect, some kind of continuity argument should apply to the classical limit of quantum systems as the value of Planck's constant tends to zero. ...more on Wikipedia about "Classical limit"
In physics, the Clebsch-Gordan coefficients are sets of numbers that arise in calculations involving addition of angular momentum under the laws of quantum mechanics. ...more on Wikipedia about "Clebsch-Gordan coefficients"
In quantum mechanics a coherent state is a specific kind of quantum state of the quantum harmonic oscillator whose dynamics most closely resemble the oscillating behaviour of a classical harmonic oscillator system. It was the first example of quantum dynamics when Erwin Schrödinger derived it in 1926 while searching for solutions of the Schrödinger equation that satisfy the correspondence principle. The quantum harmonic oscillator and hence, the coherent state, arise in the quantum theory of a wide range of physical systems. For instance, a coherent state describes the oscillating motion of the particle in a quadratic potential well. In the quantum theory of light ( quantum electrodynamics) and other bosonic quantum field theories they were introduced by the work of Roy J. Glauber. Here the coherent state of a field describes an oscillating field, the closest quantum state to a classical sinusoidal wave such as a continuous laser wave. ...more on Wikipedia about "Coherent state"
In physics, complementarity is a basic principle of quantum theory, and refers to effects such as the wave-particle duality, in which different measurements made on a system reveal it to have either particle-like or wave-like properties. Niels Bohr is usually associated with this concept; in the orthodox form, it is stated that a quantum mechanical system consisting of a boson or fermion can either behave as a particle or as wave, but never simultaneously as both. A less orthodox interpretation is the "duality condition," described by the inequality due to Englert (see Phys. Rev. Lett., Vol. 77, 2154 (1996)), which allows wave and particle attributes to co-exist, but postulates that a stronger manifestation of the particle nature leads to a weaker manifestation of the wave nature and vice versa. ...more on Wikipedia about "Complementarity (physics)"
In quantum mechanics, a complete set of commuting observables (CSCO) is a set of commuting operators whose eigenvalues completely specify the state of a system. ...more on Wikipedia about "Complete set of commuting observables"
The Compton wavelength of a particle is given by ...more on Wikipedia about "Compton wavelength"
In physics, the correspondence principle is a principle, first invoked by Niels Bohr in 1923, which states that the behavior of quantum mechanical systems reduce to classical physics in the limit of large quantum numbers. ...more on Wikipedia about "Correspondence principle"
In physics, a coupling constant, usually denoted g, is a number that determines the strength of an interaction. Usually the Lagrangian or the Hamiltonian of a system can be separated into a kinetic part and an interaction part. The coupling constant determines the strength of the interaction part with respect to the kinetic part, or between two sectors of the interaction part. For example, the electric charge of a particle is a coupling constant. ...more on Wikipedia about "Coupling constant"
An annihilation operator is the operator in that lowers the number of particles in a given state by one. ...more on Wikipedia about "Creation and annihilation operators"
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