Planck constant Plaque at the Humboldt University of Berlin: "Max Planck, discoverer of the elementary quantum of action h, taught in this building from 1889 to 1928." In 1905 the value (E), the energy of a charged atomic oscillator, was theoretically associated with the energy of the electromagnetic wave itself, representing the minimum amount of energy required to form an electromagnetic field (a "quantum"). Further investigation of quanta revealed behaviour associated with an independent unit ("particle") as opposed to an electromagnetic wave and was eventually given the term photon. The Planck relation now describes the energy of each photon in terms of the photon's frequency. This energy is extremely small in terms of ordinary experience. Since the frequency , wavelength λ, and speed of light c are related by λν = c, the Planck relation for a photon can also be expressed as The above equation leads to another relationship involving the Planck constant. Value[edit] Significance of the value[edit]
Yang–Mills existence and mass gap In mathematical physics, the Yang–Mills existence and mass gap problem is an unsolved problem and one of the seven Millennium Prize Problems defined by the Clay Mathematics Institute which has offered a prize of US$1,000,000 to the one who solves it. The problem is phrased as follows: Yang–Mills Existence and Mass Gap. and has a mass gap Δ > 0. In this statement, Yang–Mills theory is the (non-Abelian) quantum field theory underlying the Standard Model of particle physics; is Euclidean 4-space; the mass gap Δ is the mass of the least massive particle predicted by the theory. Background[edit] Quantum Yang-Mills theory with a non-abelian gauge group and no quarks is an exception, because asymptotic freedom characterizes this theory, meaning that it has a trivial UV fixed point. See also[edit] References[edit] Arthur Jaffe and Edward Witten "Quantum Yang-Mills theory." External links[edit] The Millennium Prize Problems: Yang–Mills and Mass Gap
Quantum entanglement Quantum entanglement is a physical phenomenon that occurs when pairs or groups of particles are generated or interact in ways such that the quantum state of each particle cannot be described independently – instead, a quantum state may be given for the system as a whole. Such phenomena were the subject of a 1935 paper by Albert Einstein, Boris Podolsky and Nathan Rosen,[1] describing what came to be known as the EPR paradox, and several papers by Erwin Schrödinger shortly thereafter.[2][3] Einstein and others considered such behavior to be impossible, as it violated the local realist view of causality (Einstein referred to it as "spooky action at a distance"),[4] and argued that the accepted formulation of quantum mechanics must therefore be incomplete. History[edit] However, they did not coin the word entanglement, nor did they generalize the special properties of the state they considered. Concept[edit] Meaning of entanglement[edit] Apparent paradox[edit] The hidden variables theory[edit]
Schrödinger equation In quantum mechanics, the Schrödinger equation is a partial differential equation that describes how the quantum state of some physical system changes with time. It was formulated in late 1925, and published in 1926, by the Austrian physicist Erwin Schrödinger.[1] In classical mechanics, the equation of motion is Newton's second law, and equivalent formulations are the Euler–Lagrange equations and Hamilton's equations. In quantum mechanics, the analogue of Newton's law is Schrödinger's equation for a quantum system (usually atoms, molecules, and subatomic particles whether free, bound, or localized). The concept of a state vector is a fundamental postulate of quantum mechanics. In the standard interpretation of quantum mechanics, the wave function is the most complete description that can be given to a physical system. Equation[edit] Time-dependent equation[edit] The form of the Schrödinger equation depends on the physical situation (see below for special cases). Implications[edit]
Uncertainty reigns over Heisenberg's measurement analogy A row has broken out among physicists over an analogy used by Werner Heisenberg in 1927 to make sense of his famous uncertainty principle. The analogy was largely forgotten as quantum theory became more sophisticated but has enjoyed a revival over the past decade. While several recent experiments suggest that the analogy is flawed, a team of physicists in the UK, Finland and Germany is now arguing that these experiments are not faithful to Heisenberg's original formulation. Heisenberg's uncertainty principle states that we cannot measure certain pairs of variables for a quantum object – position and momentum, say – both with arbitrary accuracy. When Heisenberg proposed the principle in 1927, he offered a simple physical picture to help it make intuitive sense. Not necessarily wrong Then in 1988 Masanao Ozawa at Nagoya University in Japan argued that Heisenberg's original relationship between error and disturbance does not represent a fundamental limit of uncertainty. Truer to Heisenberg?
Bloch sphere Bloch sphere In 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.[1] 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). In a two-dimensional Hilbert space this is simply the complex projective line, which is a geometrical sphere. The Bloch sphere is a unit 2-sphere, with each pair of antipodal points corresponding to mutually orthogonal state vectors. and Definition[edit] Given an orthonormal basis, any pure state of a two-level quantum system can be written as a superposition of the basis vectors , where the coefficient or amount of each basis vector is a complex number. to be real and non-negative. , meaning . in the following representation: with . or .
Efimov state The Efimov effect is an effect in the quantum mechanics of Few-body systems predicted by the Russian theoretical physicist V. N. Efimov[1][2] in 1970. The unusual Efimov state has an infinite number of similar states. In 2005, for the first time the research group of Rudolf Grimm and Hanns-Christoph Nägerl from the Institute for Experimental Physics (University of Innsbruck, Austria) experimentally confirmed such a state in an ultracold gas of caesium atoms. The interest in the "universal phenomena" of cold atomic gases is still growing, especially because of the long awaited experimental results.[8][9] The discipline of universality in cold atomic gases nearby the Efimov states are sometimes commonly referred to as "Efimov physics". The Efimov states are independent of the underlying physical interaction, and can in principle be observed in all quantum mechanical systems (molecular, atomic, and nuclear). References[edit] Jump up ^ В.И. External links[edit]
Matrix mechanics Matrix mechanics is a formulation of quantum mechanics created by Werner Heisenberg, Max Born, and Pascual Jordan in 1925. In some contrast to the wave formulation, it produces spectra of energy operators by purely algebraic, ladder operator, methods.[1] Relying on these methods, Pauli derived the hydrogen atom spectrum in 1926,[2] before the development of wave mechanics. Development of matrix mechanics[edit] In 1925, Werner Heisenberg, Max Born, and Pascual Jordan formulated the matrix mechanics representation of quantum mechanics. Epiphany at Helgoland[edit] In 1925 Werner Heisenberg was working in Göttingen on the problem of calculating the spectral lines of hydrogen. "It was about three o' clock at night when the final result of the calculation lay before me. The Three Fundamental Papers[edit] After Heisenberg returned to Göttingen, he showed Wolfgang Pauli his calculations, commenting at one point:[4] In the paper, Heisenberg formulated quantum theory without sharp electron orbits. W.