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Rigid Rotor
In rotordynamics, the rigid rotor is a mechanical model of rotating systems. An arbitrary rigid rotor is a 3-dimensional rigid object, such as a top. To orient such an object in space requires three angles, known as Euler angles. A special rigid rotor is the ''linear rotor'' requiring only two angles to describe, for example of a diatomic molecule. More general molecules are 3-dimensional, such as water (asymmetric rotor), ammonia (symmetric rotor), or methane (spherical rotor). Linear rotor The linear rigid rotor model consists of two point masses located at fixed distances from their center of mass. The fixed distance between the two masses and the values of the masses are the only characteristics of the rigid model. However, for many actual diatomics this model is too restrictive since distances are usually not completely fixed. Corrections on the rigid model can be made to compensate for small variations in the distance. Even in such a case the rigid rotor model is a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rotordynamics
Rotordynamics (or rotor dynamics) is a specialized branch of applied mechanics concerned with the behavior and diagnosis of rotating structures. It is commonly used to analyze the behavior of structures ranging from jet engines and steam turbines to auto engines and computer disk storage. At its most basic level, rotor dynamics is concerned with one or more mechanical structures ( rotors) supported by bearings and influenced by internal phenomena that rotate around a single axis. The supporting structure is called a stator. As the speed of rotation increases the amplitude of vibration often passes through a maximum that is called a critical speed. This amplitude is commonly excited by imbalance of the rotating structure; everyday examples include engine balance and tire balance. If the amplitude of vibration at these critical speeds is excessive, then catastrophic failure occurs. In addition to this, turbomachinery often develop instabilities which are related to the internal ma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Schrödinger Equation
The Schrödinger equation is a partial differential equation that governs the wave function of a non-relativistic quantum-mechanical system. Its discovery was a significant landmark in the development of quantum mechanics. It is named after Erwin Schrödinger, an Austrian physicist, who postulated the equation in 1925 and published it in 1926, forming the basis for the work that resulted in his Nobel Prize in Physics in 1933. Conceptually, the Schrödinger equation is the quantum counterpart of Newton's second law in classical mechanics. Given a set of known initial conditions, Newton's second law makes a mathematical prediction as to what path a given physical system will take over time. The Schrödinger equation gives the evolution over time of the wave function, the quantum-mechanical characterization of an isolated physical system. The equation was postulated by Schrödinger based on a postulate of Louis de Broglie that all matter has an associated matter wave. The equati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Microwave
Microwave is a form of electromagnetic radiation with wavelengths shorter than other radio waves but longer than infrared waves. Its wavelength ranges from about one meter to one millimeter, corresponding to frequency, frequencies between 300 MHz and 300 GHz, broadly construed. A more common definition in radio-frequency engineering is the range between 1 and 100 GHz (wavelengths between 30 cm and 3 mm), or between 1 and 3000 GHz (30 cm and 0.1 mm). In all cases, microwaves include the entire super high frequency, super high frequency (SHF) band (3 to 30 GHz, or 10 to 1 cm) at minimum. The boundaries between far infrared, terahertz radiation, microwaves, and ultra-high-frequency (UHF) are fairly arbitrary and differ between different fields of study. The prefix ' in ''microwave'' indicates that microwaves are small (having shorter wavelengths), compared to the radio waves used in prior radio technology. Frequencies in the micr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Photon
A photon () is an elementary particle that is a quantum of the electromagnetic field, including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic force. Photons are massless particles that can move no faster than the speed of light measured in vacuum. The photon belongs to the class of boson particles. As with other elementary particles, photons are best explained by quantum mechanics and exhibit wave–particle duality, their behavior featuring properties of both waves and particles. The modern photon concept originated during the first two decades of the 20th century with the work of Albert Einstein, who built upon the research of Max Planck. While Planck was trying to explain how matter and electromagnetic radiation could be in thermal equilibrium with one another, he proposed that the energy stored within a material object should be regarded as composed of an integer number of discrete, equal-sized parts. To explain the pho ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Selection Rules
In physics and chemistry, a selection rule, or transition rule, formally constrains the possible transitions of a system from one quantum state to another. Selection rules have been derived for electromagnetic transitions in molecules, in atoms, in atomic nuclei, and so on. The selection rules may differ according to the technique used to observe the transition. The selection rule also plays a role in chemical reactions, where some are formally spin-forbidden reactions, that is, reactions where the spin state changes at least once from reactants to products. In the following, mainly atomic and molecular transitions are considered. Overview In quantum mechanics the basis for a spectroscopic selection rule is the value of the ''transition moment integral'' :m_ = \int \psi_1^* \, \mu \, \psi_2 \, \mathrm\tau, where \psi_1 and \psi_2 are the wave functions of the two states, "state 1" and "state 2", involved in the transition, and is the transition moment operator. Thi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Number
In 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, azimuthal, magnetic, and 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 of quarks, which have no classical correspondence. Quantum numbers are closely related to eigenvalues of observables. When the corresponding observable commutes with the Hamiltonian of the system, the quantum number is said to be " good", and acts as a constant of motion in the quantum dynamics. History Electronic quantum numbers In the era of the old quantum theory, starting from Max Planck's proposal of quanta in his model of blackbody radiation (1900) and Albert Einstein's adaptation o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wavenumber
In the physical sciences, the wavenumber (or wave number), also known as repetency, is the spatial frequency of a wave. Ordinary wavenumber is defined as the number of wave cycles divided by length; it is a physical quantity with dimension of reciprocal length, expressed in SI units of cycles per metre or reciprocal metre (m−1). Angular wavenumber, defined as the wave phase divided by time, is a quantity with dimension of angle per length and SI units of radians per metre. They are analogous to temporal frequency, respectively the '' ordinary frequency'', defined as the number of wave cycles divided by time (in cycles per second or reciprocal seconds), and the ''angular frequency'', defined as the phase angle divided by time (in radians per second). In multidimensional systems, the wavenumber is the magnitude of the '' wave vector''. The space of wave vectors is called ''reciprocal space''. Wave numbers and wave vectors play an essential role in optics and the physics ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reciprocal Length
Reciprocal length or inverse length is a quantity or measurement used in several branches of science and mathematics, defined as the reciprocal of length. Common units used for this measurement include the reciprocal metre or inverse metre (symbol: m−1), the reciprocal centimetre or inverse centimetre (symbol: cm−1). In optics, the dioptre is a unit equivalent to reciprocal metre. List of quantities Quantities measured in reciprocal length include: * absorption coefficient or attenuation coefficient, in materials science * curvature of a line, in mathematics * gain, in laser physics * magnitude of vectors in reciprocal space, in crystallography * more generally any spatial frequency e.g. in cycles per unit length * optical power of a lens, in optics * rotational constant of a rigid rotor, in quantum mechanics * wavenumber, or magnitude of a wavevector, in spectroscopy * density of a linear feature in hydrology and other fields; see kilometre per square kil ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spherical Harmonic
In mathematics and Outline of physical science, physical science, spherical harmonics are special functions defined on the surface of a sphere. They are often employed in solving partial differential equations in many scientific fields. The table of spherical harmonics contains a list of common spherical harmonics. Since the spherical harmonics form a complete set of orthogonal functions and thus an orthonormal basis, every function defined on the surface of a sphere can be written as a sum of these spherical harmonics. This is similar to periodic functions defined on a circle that can be expressed as a sum of Trigonometric functions, circular functions (sines and cosines) via Fourier series. Like the sines and cosines in Fourier series, the spherical harmonics may be organized by (spatial) angular frequency, as seen in the rows of functions in the illustration on the right. Further, spherical harmonics are basis functions for irreducible representations of Rotation group SO(3), ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hydrogen Atom
A hydrogen atom is an atom of the chemical element hydrogen. The electrically neutral hydrogen atom contains a single positively charged proton in the nucleus, and a single negatively charged electron bound to the nucleus by the Coulomb force. Atomic hydrogen constitutes about 75% of the baryonic mass of the universe. In everyday life on Earth, isolated hydrogen atoms (called "atomic hydrogen") are extremely rare. Instead, a hydrogen atom tends to combine with other atoms in compounds, or with another hydrogen atom to form ordinary (diatomic) hydrogen gas, H2. "Atomic hydrogen" and "hydrogen atom" in ordinary English use have overlapping, yet distinct, meanings. For example, a water molecule contains two hydrogen atoms, but does not contain atomic hydrogen (which would refer to isolated hydrogen atoms). Atomic spectroscopy shows that there is a discrete infinite set of states in which a hydrogen (or any) atom can exist, contrary to the predictions of classical physics. At ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reduced Planck Constant
The Planck constant, or Planck's constant, denoted by h, is a fundamental physical constant of foundational importance in quantum mechanics: a photon's energy is equal to its frequency multiplied by the Planck constant, and the wavelength of a matter wave equals the Planck constant divided by the associated particle momentum. The constant was postulated by Max Planck in 1900 as a proportionality constant needed to explain experimental black-body radiation. Planck later referred to the constant as the "quantum of action". In 1905, Albert Einstein associated the "quantum" or minimal element of the energy to the electromagnetic wave itself. Max Planck received the 1918 Nobel Prize in Physics "in recognition of the services he rendered to the advancement of Physics by his discovery of energy quanta". In metrology, the Planck constant is used, together with other constants, to define the kilogram, the SI unit of mass. The SI units are defined in such a way that, when the Pla ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
