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Bohr–Sommerfeld Model
The Bohr–Sommerfeld model (also known as the Sommerfeld model or Bohr–Sommerfeld theory) was an extension of the Bohr model to allow elliptical orbits of electrons around an atomic nucleus. Bohr–Sommerfeld theory is named after Danish physicist Niels Bohr and German physicist Arnold Sommerfeld. Sommerfeld showed that, if electronic orbits are ellipse, elliptical instead of circular (as in Bohr's model of the atom), the fine-structure of the hydrogen atom can be described. The Bohr–Sommerfeld model added to the quantized angular momentum condition of the Bohr model with a radial quantization (condition by William Wilson (English academic), William Wilson, the Wilson–Sommerfeld quantization condition): : \int_0^T p_r \,dq_r = n h, where ''pr'' is the radial momentum canonically conjugate to the coordinate ''q'', which is the radial position, and ''T'' is one full orbital period. The integral is the Action (physics), action of action-angle coordinates. This cond ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Radium Kramer Holst 1923
Radium is a chemical element; it has chemical symbol, symbol Ra and atomic number 88. It is the sixth element in alkaline earth metal, group 2 of the periodic table, also known as the alkaline earth metals. Pure radium is silvery-white, but it readily reacts with nitrogen (rather than oxygen) upon exposure to air, forming a black surface layer of radium nitride (Ra3N2). All isotopes of radium are radioactive, the most stable isotope being radium-226 with a half-life of 1,600 years. When radium decays, it emits ionizing radiation as a by-product, which can excite fluorescent chemicals and cause radioluminescence. For this property, it was widely used in Self-luminous paint, self-luminous paints following its discovery. Of the Radionuclide, radioactive elements that occur in quantity, radium is considered particularly Toxicity, toxic, and it is Carcinogen, carcinogenic due to the radioactivity of both it and its immediate decay product radon as well as its tendency to B ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Atomic Emission Spectrum
The emission spectrum of a chemical element or chemical compound is the Spectrum (physical sciences), spectrum of frequencies of electromagnetic radiation emitted due to electrons making a atomic electron transition, transition from a high energy state to a lower energy state. The photon energy of the emitted photons is equal to the energy difference between the two states. There are many possible electron transitions for each atom, and each transition has a specific energy difference. This collection of different transitions, leading to different radiated wavelengths, make up an emission spectrum. Each element's emission spectrum is unique. Therefore, spectroscopy can be used to identify elements in matter of unknown composition. Similarly, the emission spectra of molecules can be used in chemical analysis of substances. Emission In physics, emission is the process by which a higher energy quantum mechanical state of a particle becomes converted to a lower one through the emis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Magnetic Field
A magnetic field (sometimes called B-field) is a physical field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular to its own velocity and to the magnetic field. A permanent magnet's magnetic field pulls on ferromagnetic materials such as iron, and attracts or repels other magnets. In addition, a nonuniform magnetic field exerts minuscule forces on "nonmagnetic" materials by three other magnetic effects: paramagnetism, diamagnetism, and antiferromagnetism, although these forces are usually so small they can only be detected by laboratory equipment. Magnetic fields surround magnetized materials, electric currents, and electric fields varying in time. Since both strength and direction of a magnetic field may vary with location, it is described mathematically by a function (mathematics), function assigning a Euclidean vector, vector to each point of space, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Energy Levels
A quantum mechanics, quantum mechanical system or particle that is bound state, bound—that is, confined spatially—can only take on certain discrete values of energy, called energy levels. This contrasts with classical mechanics, classical particles, which can have any amount of energy. The term is commonly used for the energy levels of the electrons in atoms, ions, or molecules, which are bound by the electric field of the atomic nucleus, nucleus, but can also refer to energy levels of nuclei or molecular vibration, vibrational or rotational energy levels in molecules. The energy spectrum of a system with such discrete energy levels is said to be Quantization (physics), quantized. In chemistry and atomic physics, an electron shell, or principal energy level, may be thought of as the orbit of one or more electrons around an atom's atomic nucleus, nucleus. The closest shell to the nucleus is called the "1 shell" (also called "K shell"), followed by the "2 shell" (or "L shell"), ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stern–Gerlach Experiment
In quantum physics, the Stern–Gerlach experiment demonstrated that the spatial orientation of angular momentum is quantization (physics), quantized. Thus an Atomic spacing, atomic-scale system was shown to have intrinsically quantum properties. In the original experiment, silver atoms were sent through a spatially-varying magnetic field, which Deflection (physics), deflected them before they struck a detector screen, such as a glass slide. Particles with non-zero magnetic moment were deflected, owing to the magnetic field spatial gradient, gradient, from a straight path. The screen revealed discrete points of accumulation, rather than a continuous distribution, owing to their quantized Spin (physics), spin. Historically, this experiment was decisive in convincing physicists of the reality of angular-momentum quantization in all atomic-scale systems. After its conception by Otto Stern in 1921, the experiment was first successfully conducted with Walther Gerlach in early 1922. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Path Integral Formulation
The path integral formulation is a description in quantum mechanics that generalizes the stationary action principle of classical mechanics. It replaces the classical notion of a single, unique classical trajectory for a system with a sum, or functional integral, over an infinity of quantum-mechanically possible trajectories to compute a quantum amplitude. This formulation has proven crucial to the subsequent development of theoretical physics, because manifest Lorentz covariance (time and space components of quantities enter equations in the same way) is easier to achieve than in the operator formalism of canonical quantization. Unlike previous methods, the path integral allows one to easily change coordinates between very different canonical descriptions of the same quantum system. Another advantage is that it is in practice easier to guess the correct form of the Lagrangian of a theory, which naturally enters the path integrals (for interactions of a certain type, these ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Chaos
Quantum chaos is a branch of physics focused on how chaotic classical dynamical systems can be described in terms of quantum theory. The primary question that quantum chaos seeks to answer is: "What is the relationship between quantum mechanics and classical chaos?" The correspondence principle states that classical mechanics is the classical limit of quantum mechanics, specifically in the limit as the ratio of the Planck constant to the action of the system tends to zero. If this is true, then there must be quantum mechanisms underlying classical chaos (although this may not be a fruitful way of examining classical chaos). If quantum mechanics does not demonstrate an exponential sensitivity to initial conditions, how can exponential sensitivity to initial conditions arise in classical chaos, which must be the correspondence principle limit of quantum mechanics? Michael Berry, "Quantum Chaology", pp 104-5 of ''Quantum: a guide for the perplexed'' by Jim Al-Khalili (Weidenfeld ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Martin Gutzwiller
Martin Charles Gutzwiller (12 October 1925 – 3 March 2014) was a Swiss-American physicist, known for his work on field theory, quantum chaos, and complex systems. He spent most of his career at IBM Research, and was also an adjunct professor of physics at Yale University. Biography Gutzwiller was born on October 12, 1925, in the Swiss city of Basel. He completed a Diploma degree from ETH Zurich, where he studied quantum physics under Wolfgang Pauli. He then went to the University of Kansas and completed a Ph.D under Max Dresden. After graduation, he worked on microwave engineering for Brown, Boveri & Cie, on geophysics for Shell Oil, and eventually for IBM Research in Switzerland, New York City, and Yorktown Heights, until his retirement in 1993. He also held temporary teaching appointments at Columbia University, ETH Zurich, Paris-Orsay, and Stockholm. He was Vice Chair for the Committee on Mathematical Physics, of the International Union of Pure and Applied Phy ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Einstein–Brillouin–Keller Method
The Einstein–Brillouin–Keller (EBK) method is a semiclassical technique (named after Albert Einstein, Léon Brillouin, and Joseph B. Keller) used to compute eigenvalues in quantum-mechanical systems. EBK quantization is an improvement from Bohr-Sommerfeld quantization which did not consider the caustic phase jumps at classical turning points. This procedure is able to reproduce exactly the spectrum of the 3D harmonic oscillator, particle in a box, and even the relativistic fine structure of the hydrogen atom. In 1976–1977, Michael Berry and M. Tabor derived an extension to Gutzwiller trace formula for the density of states of an integrable system starting from EBK quantization. There have been a number of recent results on computational issues related to this topic, for example, the work of Eric J. Heller and Emmanuel David Tannenbaum using a partial differential equation gradient descent approach. Procedure Given a separable classical system defined by coordinate ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Joseph Keller
Joseph Bishop Keller (July 31, 1923 – September 7, 2016) was an American mathematician who specialized in applied mathematics. He was best known for his work on the "geometrical theory of diffraction" (GTD). Early life and education Born in Paterson, New Jersey on July 31, 1923, Keller attended Eastside High School, where he was a member of the math team. After earning his undergraduate degree in 1943 at New York University, Keller obtained his PhD in 1948 from NYU under the supervision of Richard Courant. He was a professor of mathematics in the Courant Institute at New York University until 1979. Then he was Professor of Mathematics and Mechanical Engineering at Stanford University until 1993, when he became professor emeritus. Research Keller worked on the application of mathematics to problems in science and engineering, such as wave propagation. He contributed to the Einstein–Brillouin–Keller method for computing eigenvalues in quantum mechanical systems. Awar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spin (physics)
Spin is an Intrinsic and extrinsic properties, intrinsic form of angular momentum carried by elementary particles, and thus by List of particles#Composite particles, composite particles such as hadrons, atomic nucleus, atomic nuclei, and atoms. Spin is quantized, and accurate models for the interaction with spin require relativistic quantum mechanics or quantum field theory. The existence of electron spin angular momentum is inferred from experiments, such as the Stern–Gerlach experiment, in which silver atoms were observed to possess two possible discrete angular momenta despite having no orbital angular momentum. The relativistic spin–statistics theorem connects electron spin quantization to the Pauli exclusion principle: observations of exclusion imply half-integer spin, and observations of half-integer spin imply exclusion. Spin is described mathematically as a vector for some particles such as photons, and as a spinor or bispinor for other particles such as electrons. Sp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Zeeman Effect
The Zeeman effect () is the splitting of a spectral line into several components in the presence of a static magnetic field. It is caused by the interaction of the magnetic field with the magnetic moment of the atomic electron associated with its Angular momentum, orbital motion and Spin (physics), spin; this interaction shifts some orbital energies more than others, resulting in the split spectrum. The effect is named after the Netherlands, Dutch physicist Pieter Zeeman, who discovered it in 1896 and received a Nobel Prize in Physics for this discovery. It is analogous to the Stark effect, the splitting of a spectral line into several components in the presence of an electric field. Also, similar to the Stark effect, transitions between different components have, in general, different intensities, with some being entirely forbidden (in the dipole approximation), as governed by the selection rules. Since the distance between the Zeeman sub-levels is a function of magnetic field ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
