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Total Angular Momentum
In quantum mechanics, the total angular momentum quantum number parametrises the total angular momentum of a given particle, by combining its orbital angular momentum and its intrinsic angular momentum (i.e., its spin). If s is the particle's spin angular momentum and ℓ its orbital angular momentum vector, the total angular momentum j is \mathbf j = \mathbf s + \boldsymbol ~. The associated quantum number is the main total angular momentum quantum number ''j''. It can take the following range of values, jumping only in integer steps: \vert \ell - s\vert \le j \le \ell + s where ''ℓ'' is the azimuthal quantum number (parameterizing the orbital angular momentum) and ''s'' is the spin quantum number (parameterizing the spin). The relation between the total angular momentum vector j and the total angular momentum quantum number ''j'' is given by the usual relation (see angular momentum quantum number) \Vert \mathbf j \Vert = \sqrt \, \hbar The vector's ''z''-projection i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Mechanics
Quantum mechanics is the fundamental physical Scientific theory, theory that describes the behavior of matter and of light; its unusual characteristics typically occur at and below the scale of atoms. Reprinted, Addison-Wesley, 1989, It is the foundation of all quantum physics, which includes quantum chemistry, quantum field theory, quantum technology, and quantum information science. Quantum mechanics can describe many systems that classical physics cannot. Classical physics can describe many aspects of nature at an ordinary (macroscopic and Microscopic scale, (optical) microscopic) scale, but is not sufficient for describing them at very small submicroscopic (atomic and subatomic) scales. Classical mechanics can be derived from quantum mechanics as an approximation that is valid at ordinary scales. Quantum systems have Bound state, bound states that are Quantization (physics), quantized to Discrete mathematics, discrete values of energy, momentum, angular momentum, and ot ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Azimuthal Quantum Number
In quantum mechanics, the azimuthal quantum number is a quantum number for an atomic orbital that determines its angular momentum operator, orbital angular momentum and describes aspects of the angular shape of the orbital. The azimuthal quantum number is the second of a set of quantum numbers that describe the unique quantum state of an electron (the others being the principal quantum number , the magnetic quantum number , and the spin quantum number ). For a given value of the principal quantum number (''electron shell''), the possible values of are the integers from 0 to . For instance, the shell has only orbitals with \ell=0, and the shell has only orbitals with \ell=0, and \ell=1. For a given value of the azimuthal quantum number , the possible values of the magnetic quantum number are the integers from to , including 0. In addition, the spin quantum number can take two distinct values. The set of orbitals associated with a particular value of are som ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Numbers
In Quantum mechanics, quantum physics and chemistry, quantum numbers are quantities that characterize the possible states of the system. To fully specify the state of the electron in a hydrogen atom, four quantum numbers are needed. The traditional set of quantum numbers includes the Principal quantum number, principal, Azimuthal quantum number, azimuthal, Magnetic quantum number, magnetic, and Spin quantum number, spin quantum numbers. To describe other systems, different quantum numbers are required. For subatomic particles, one needs to introduce new quantum numbers, such as the flavour (particle physics), flavour of quarks, which have no classical correspondence. Quantum numbers are closely related to eigenvalues of observables. When the corresponding observable commutes with the Hamiltonian (quantum mechanics), Hamiltonian of the system, the quantum number is said to be "Good quantum number, good", and acts as a constant of motion in the quantum dynamics. History Elect ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Atomic Physics
Atomic physics is the field of physics that studies atoms as an isolated system of electrons and an atomic nucleus. Atomic physics typically refers to the study of atomic structure and the interaction between atoms. It is primarily concerned with the way in which electrons are arranged around the nucleus and the processes by which these arrangements change. This comprises ions, neutral atoms and, unless otherwise stated, it can be assumed that the term ''atom'' includes ions. The term ''atomic physics'' can be associated with nuclear power and nuclear weapons, due to the synonymous use of ''atomic'' and ''nuclear'' in standard English. Physicists distinguish between atomic physics—which deals with the atom as a system consisting of a nucleus and electrons—and nuclear physics, which studies nuclear reactions and special properties of atomic nuclei. As with many scientific fields, strict delineation can be highly contrived and atomic physics is often considered in the w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Angular Momentum
Angular momentum (sometimes called moment of momentum or rotational momentum) is the rotational analog of Momentum, linear momentum. It is an important physical quantity because it is a Conservation law, conserved quantity – the total angular momentum of a closed system remains constant. Angular momentum has both a direction (geometry), direction and a magnitude, and both are conserved. Bicycle and motorcycle dynamics, Bicycles and motorcycles, flying discs, Rifling, rifled bullets, and gyroscopes owe their useful properties to conservation of angular momentum. Conservation of angular momentum is also why hurricanes form spirals and neutron stars have high rotational rates. In general, conservation limits the possible motion of a system, but it does not uniquely determine it. The three-dimensional angular momentum for a point particle is classically represented as a pseudovector , the cross product of the particle's position vector (relative to some origin) and its mo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Albert Messiah
Albert Messiah (23 September 1921, Nice – 17 April 2013, Paris) was a French physicist. He studied at the Ecole Polytechnique. He spent the Second World War in the Free France forces: he embarked on 22 June 1940 at Saint-Jean-de-Luz for England and participated in the Battle of Dakar with Charles de Gaulle in September 1940. He joined the Free French Forces in Chad, and the 2nd Armored Division in September 1944, and participated in the assault of Hitler's Eagle's nest at Berchtesgaden in 1945. As a French Jew who escaped France to fight in the Free French Army of de Gaulle, he was awarded a grant to study and work at the Institute for Advanced Study in Princeton, New Jersey in the US. The seminars at the Institute were incomprehensible to Messiah who had only a high-school education in physics, and he became depressed to the extent that he considered abandoning his plans to become a physicist. He met Robert Marshak at a meeting of the American Physical Society in Washingt ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rotational Spectroscopy
Rotational spectroscopy is concerned with the measurement of the energies of transitions between quantized rotational states of molecules in the gas phase. The rotational spectrum (power spectral density vs. rotational frequency) of chemical polarity, polar molecules can be measured in Absorption (optics), absorption or Emission (electromagnetic radiation), emission by microwave spectroscopy or by far infrared spectroscopy. The rotational spectra of non-polar molecules cannot be observed by those methods, but can be observed and measured by Raman spectroscopy. Rotational spectroscopy is sometimes referred to as ''pure'' rotational spectroscopy to distinguish it from rotational-vibrational spectroscopy where changes in rotational energy occur together with changes in vibrational energy, and also from ro-vibronic spectroscopy (or just vibronic spectroscopy) where rotational, vibrational and electronic energy changes occur simultaneously. For rotational spectroscopy, molecules are cl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Angular Momentum Diagrams (quantum Mechanics)
In quantum mechanics and its applications to quantum many-particle systems, notably quantum chemistry, angular momentum diagrams, or more accurately from a mathematical viewpoint angular momentum graphs, are a diagrammatic method for representing angular momentum quantum states of a quantum system allowing calculations to be done symbolically. More specifically, the arrows encode angular momentum states in bra–ket notation and include the abstract nature of the state, such as tensor products and transformation rules. The notation parallels the idea of Penrose graphical notation and Feynman diagrams. The diagrams consist of arrows and vertices with quantum numbers as labels, hence the alternative term "graphs". The sense of each arrow is related to Hermitian conjugation, which roughly corresponds to time reversal of the angular momentum states (cf. Schrödinger equation). The diagrammatic notation is a considerably large topic in its own right with a number of specialized feat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Clebsch–Gordan Coefficients
In physics, the Clebsch–Gordan (CG) coefficients are numbers that arise in angular momentum coupling in quantum mechanics. They appear as the expansion coefficients of total angular momentum eigenstates in an uncoupled tensor product basis. In more mathematical terms, the CG coefficients are used in representation theory, particularly of compact Lie groups, to perform the explicit direct sum decomposition of the tensor product of two irreducible representations (i.e., a reducible representation into irreducible representations, in cases where the numbers and types of irreducible components are already known abstractly). The name derives from the German mathematicians Alfred Clebsch and Paul Gordan, who encountered an equivalent problem in invariant theory. From a vector calculus perspective, the CG coefficients associated with the SO(3) group can be defined simply in terms of integrals of products of spherical harmonics and their complex conjugates. The addition of spins in quant ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Angular Momentum Coupling
In quantum mechanics, angular momentum coupling is the procedure of constructing eigenstates of total angular momentum out of eigenstates of separate angular momenta. For instance, the orbit and spin of a single particle can interact through spin–orbit interaction, in which case the complete physical picture must include spin–orbit coupling. Or two charged particles, each with a well-defined angular momentum, may interact by Electrostatic#Coulomb's law, Coulomb forces, in which case coupling of the two one-particle angular momenta to a total angular momentum is a useful step in the solution of the two-particle Schrödinger equation. In both cases the separate angular momenta are no longer constants of motion, but the sum of the two angular momenta usually still is. Angular momentum coupling in atoms is of importance in atomic spectroscopy. Angular momentum coupling of electron spins is of importance in quantum chemistry. Also in the nuclear shell model angular momentum co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spin Quantum Number
In physics and chemistry, the spin quantum number is a quantum number (designated ) that describes the intrinsic angular momentum (or spin angular momentum, or simply ''spin'') of an electron or other particle. It has the same value for all particles of the same type, such as = for all electrons. It is an integer for all bosons, such as photons, and a half-odd-integer for all fermions, such as electrons and protons. The component of the spin along a specified axis is given by the spin magnetic quantum number, conventionally written . The value of is the component of spin angular momentum, in units of the reduced Planck constant , parallel to a given direction (conventionally labelled the –axis). It can take values ranging from + to − in integer increments. For an electron, can be either or . Nomenclature The phrase ''spin quantum number'' refers to quantized spin angular momentum. The symbol is used for the spin quantum number, and is described as the s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Magnetic Quantum Number
In atomic physics, a magnetic quantum number is a quantum number used to distinguish quantum states of an electron or other particle according to its angular momentum along a given axis in space. The orbital magnetic quantum number ( or ) distinguishes the orbitals available within a given subshell of an atom. It specifies the component of the orbital angular momentum that lies along a given axis, conventionally called the ''z''-axis, so it describes the orientation of the orbital in space. The spin magnetic quantum number specifies the ''z''-axis component of the spin angular momentum for a particle having spin quantum number . For an electron, is , and is either + or −, often called "spin-up" and "spin-down", or α and β. The term ''magnetic'' in the name refers to the magnetic dipole moment associated with each type of angular momentum, so states having different magnetic quantum numbers shift in energy in a magnetic field according to the Zeeman effect. The four quant ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
