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Van Vleck Paramagnetism
In condensed matter and atomic physics, Van Vleck paramagnetism refers to a positive and temperature-independent contribution to the magnetic susceptibility of a material, derived from second order corrections to the Zeeman effect, Zeeman interaction. The quantum mechanical theory was developed by John Hasbrouck Van Vleck between the 1920s and the 1930s to explain the magnetic response of gaseous nitric oxide () and of rare-earth salts. Alongside other magnetic effects like Paul Langevin's formulas for paramagnetism (Curie's law) and diamagnetism, Van Vleck discovered an additional paramagnetic contribution of the same order as Langevin's diamagnetism. Van Vleck contribution is usually important for systems with one electron short of being half filled and this contribution vanishes for elements with Electron configuration, closed shells. Description The magnetization of a material under an external small magnetic field \mathbf is approximately described by :\mathbf=\chi\mathbf wh ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Condensed Matter
Condensed matter physics is the field of physics that deals with the macroscopic and microscopic physical properties of matter, especially the solid and liquid phases, that arise from electromagnetic forces between atoms and electrons. More generally, the subject deals with condensed phases of matter: systems of many constituents with strong interactions among them. More exotic condensed phases include the superconducting phase exhibited by certain materials at extremely low cryogenic temperatures, the ferromagnetic and antiferromagnetic phases of spins on crystal lattices of atoms, the Bose–Einstein condensates found in ultracold atomic systems, and liquid crystals. Condensed matter physicists seek to understand the behavior of these phases by experiments to measure various material properties, and by applying the physical laws of quantum mechanics, electromagnetism, statistical mechanics, and other physics theories to develop mathematical models and predict the propert ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Thermodynamic Temperature
Thermodynamic temperature, also known as absolute temperature, is a physical quantity which measures temperature starting from absolute zero, the point at which particles have minimal thermal motion. Thermodynamic temperature is typically expressed using the Kelvin scale, where the unit of measurement is the ''kelvin'' (unit symbol: K). The Kelvin scale uses the same degree interval as the Celsius scale but is offset so that 0 K corresponds to absolute zero. For comparison, a temperature of 295 K corresponds to 21.85 °C and 71.33 °F. Another absolute scale of temperature is the Rankine scale, which is based on the Fahrenheit degree interval. Historically, thermodynamic temperature was defined by Lord Kelvin in terms of a macroscopic relation between Work (thermodynamics), thermodynamic work and Heat, heat transfer as defined in thermodynamics, but the kelvin was redefined by international agreement in 2019 in terms of phenomena that are now understood as man ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Brillouin And Langevin Functions
The Brillouin and Langevin functions are a pair of special functions that appear when studying an idealized paramagnetic material in statistical mechanics. These functions are named after French physicists Paul Langevin and Léon Brillouin who contributed to the microscopic understanding of magnetic properties of matter. The Langevin function is derived using statistical mechanics, and describes how magnetic dipoles are aligned by an applied field. The Brillouin function was developed later to give an explanation that considers quantum physics. The Langevin function could then be a seen as a special case of the more general Brillouin function if the quantum number J would be infinite (J \to \infty ). Brillouin function for paramagnetism The Brillouin function arises when studying magnetization of an ideal paramagnetism, paramagnet. In particular, it describes the dependency of the magnetization M on the applied magnetic field B, defined by the following equation: The function ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wigner–Eckart Theorem
The Wigner–Eckart theorem is a theorem of representation theory and quantum mechanics. It states that matrix elements of spherical tensor operators in the basis of angular momentum eigenstates can be expressed as the product of two factors, one of which is independent of angular momentum orientation, and the other a Clebsch–Gordan coefficient. The name derives from physicists Eugene Wigner and Carl Eckart, who developed the formalism as a link between the symmetry transformation groups of space (applied to the Schrödinger equations) and the laws of conservation of energy, momentum, and angular momentum.Eckart Biography – The National Academies Press. Mathematically, the Wigner–Eckart theorem is generally stated in the following way. Given a tensor operator and two states of angular mo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Landé G-factor
In physics, the Landé ''g''-factor is a particular example of a ''g''-factor, namely for an electron with both spin and orbital angular momenta. It is named after Alfred Landé, who first described it in 1921. In atomic physics, the Landé ''g''-factor is a multiplicative term appearing in the expression for the energy levels of an atom in a weak magnetic field. The quantum states of electrons in atomic orbitals are normally degenerate in energy, with these degenerate states all sharing the same angular momentum. When the atom is placed in a weak magnetic field, however, the degeneracy is lifted. Description The factor comes about during the calculation of the first-order perturbation in the energy of an atom when a weak uniform magnetic field (that is, weak in comparison to the system's internal magnetic field) is applied to the system. Formally we can write the factor as, :g_J= g_L\frac+g_S\frac. The orbital g_L is equal to 1, and under the approximation g_S = 2 , th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Paschen-Back 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 orbital motion and spin; this interaction shifts some orbital energies more than others, resulting in the split spectrum. The effect is named after the 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 strength, this effect can be used to measure ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Perturbation Theory (quantum Mechanics)
In quantum mechanics, perturbation theory is a set of approximation schemes directly related to mathematical perturbation for describing a complicated quantum system in terms of a simpler one. The idea is to start with a simple system for which a mathematical solution is known, and add an additional "perturbing" Hamiltonian representing a weak disturbance to the system. If the disturbance is not too large, the various physical quantities associated with the perturbed system (e.g. its energy levels and eigenstates) can be expressed as "corrections" to those of the simple system. These corrections, being small compared to the size of the quantities themselves, can be calculated using approximate methods such as asymptotic series. The complicated system can therefore be studied based on knowledge of the simpler one. In effect, it is describing a complicated unsolved system using a simple, solvable system. Approximate Hamiltonians Perturbation theory is an important tool for de ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Position Operator
In quantum mechanics, the position operator is the operator that corresponds to the position observable of a particle. When the position operator is considered with a wide enough domain (e.g. the space of tempered distributions), its eigenvalues are the possible position vectors of the particle. In one dimension, if by the symbol , x \rangle we denote the unitary eigenvector of the position operator corresponding to the eigenvalue x, then, , x \rangle represents the state of the particle in which we know with certainty to find the particle itself at position x. Therefore, denoting the position operator by the symbol X we can write X, x\rangle = x , x\rangle, for every real position x. One possible realization of the unitary state with position x is the Dirac delta (function) distribution centered at the position x, often denoted by \delta_x. In quantum mechanics, the ordered (continuous) family of all Dirac distributions, i.e. the family \delta = (\delta_x)_, is called ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Angular Momentum Operator
In quantum mechanics, the angular momentum operator is one of several related operators analogous to classical angular momentum. The angular momentum operator plays a central role in the theory of atomic and molecular physics and other quantum problems involving rotational symmetry. Being an observable, its eigenfunctions represent the distinguishable physical states of a system's angular momentum, and the corresponding eigenvalues the observable experimental values. When applied to a mathematical representation of the state of a system, yields the same state multiplied by its angular momentum value if the state is an eigenstate (as per the eigenstates/eigenvalues equation). In both classical and quantum mechanical systems, angular momentum (together with linear momentum and energy) is one of the three fundamental properties of motion.Introductory Quantum Mechanics, Richard L. Liboff, 2nd Edition, There are several angular momentum operators: total angular momentum (usually den ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electron Rest Mass
In particle physics, the electron mass (symbol: ) is the mass of a stationary electron, also known as the invariant mass of the electron. It is one of the fundamental constants of physics. It has a value of about or about , which has an energy-equivalent of about or about . Terminology The term "rest mass" is sometimes used because in special relativity the mass of an object can be said to increase in a frame of reference that is moving relative to that object (or if the object is moving in a given frame of reference). Most practical measurements are carried out on moving electrons. If the electron is moving at a relativistic velocity, any measurement must use the correct expression for mass. Such correction becomes substantial for electrons accelerated by voltages of over . For example, the relativistic expression for the total energy, , of an electron moving at speed is E = \gamma m_\mathrm c^2 , where * is the speed of light; * is the Lorentz factor, \gamma = 1/\sqr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Elementary Charge
The elementary charge, usually denoted by , is a fundamental physical constant, defined as the electric charge carried by a single proton (+1 ''e'') or, equivalently, the magnitude of the negative electric charge carried by a single electron, which has charge −1 . In SI units, the coulomb is defined such that the value of the elementary charge is exactly or 160.2176634 zeptocoulombs (zC). Since the 2019 revision of the SI, the seven SI base units are defined in terms of seven fundamental physical constants, of which the elementary charge is one. In the centimetre–gram–second system of units (CGS), the corresponding quantity is . Robert A. Millikan and Harvey Fletcher's oil drop experiment first directly measured the magnitude of the elementary charge in 1909, differing from the modern accepted value by just 0.6%. Under assumptions of the then-disputed atomic theory, the elementary charge had also been indirectly inferred to ~3% accuracy from blackb ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
G-factor (physics)
A ''g''-factor (also called ''g'' value) is a dimensionless quantity that characterizes the magnetic moment and angular momentum of an atom, a particle or the nucleus. It is the ratio of the magnetic moment (or, equivalently, the gyromagnetic ratio) of a particle to that expected of a classical particle of the same charge and angular momentum. In nuclear physics, the nuclear magneton replaces the classically expected magnetic moment (or gyromagnetic ratio) in the definition. The two definitions coincide for the proton. Definition Dirac particle The spin magnetic moment of a charged, spin-1/2 particle that does not possess any internal structure (a Dirac particle) is given by \boldsymbol \mu = g \mathbf S , where ''μ'' is the spin magnetic moment of the particle, ''g'' is the ''g''-factor of the particle, ''e'' is the elementary charge, ''m'' is the mass of the particle, and S is the spin angular momentum of the particle (with magnitude ''ħ''/2 for Dirac particles). B ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
