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Quantum LC Circuit
An LC circuit can be quantized using the same methods as for the quantum harmonic oscillator. An LC circuit is a variety of resonant circuit, and consists of an inductor, represented by the letter L, and a capacitor, represented by the letter C. When connected together, an electric current can alternate between them at the circuit's resonant frequency: :\omega = \sqrt where L is the inductance in henries, and C is the capacitance in farads. The angular frequency \omega\, has units of radians per second. A capacitor stores energy in the electric field between the plates, which can be written as follows: :U_C=\frac C V^2 =\frac Where Q is the net charge on the capacitor, calculated as : Q(t) = \int_^t I(\tau) d\tau Likewise, an inductor stores energy in the magnetic field depending on the current, which can be written as follows: :U_L=\frac L I^2 =\frac Where \phi is the branch flux, defined as :\phi(t) \equiv \int_^t V(\tau) d\tau Since charge and flux are canonically ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Harmonic Potential
The quantum harmonic oscillator is the quantum-mechanical analog of the classical harmonic oscillator. Because an arbitrary smooth potential can usually be approximated as a harmonic potential at the vicinity of a stable equilibrium point, it is one of the most important model systems in quantum mechanics. Furthermore, it is one of the few quantum-mechanical systems for which an exact, analytical solution is known. One-dimensional harmonic oscillator Hamiltonian and energy eigenstates The Hamiltonian of the particle is: \hat H = \frac + \frac k ^2 = \frac + \frac m \omega^2 ^2 \, , where is the particle's mass, is the force constant, \omega = \sqrt is the angular frequency of the oscillator, \hat is the position operator (given by in the coordinate basis), and \hat is the momentum operator (given by \hat p = -i \hbar \, \partial / \partial x in the coordinate basis). The first term in the Hamiltonian represents the kinetic energy of the particle, and the second term ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Electromagnetic Resonator
An LC circuit can be quantized using the same methods as for the quantum harmonic oscillator. An LC circuit is a variety of resonant circuit, and consists of an inductor, represented by the letter L, and a capacitor, represented by the letter C. When connected together, an electric current can alternate between them at the circuit's resonant frequency: :\omega = \sqrt where L is the inductance in henries, and C is the capacitance in farads. The angular frequency \omega\, has units of radians per second. A capacitor stores energy in the electric field between the plates, which can be written as follows: :U_C=\frac C V^2 =\frac Where Q is the net charge on the capacitor, calculated as : Q(t) = \int_^t I(\tau) d\tau Likewise, an inductor stores energy in the magnetic field depending on the current, which can be written as follows: :U_L=\frac L I^2 =\frac Where \phi is the branch flux, defined as :\phi(t) \equiv \int_^t V(\tau) d\tau Since charge and flux are canonically ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Harmonic Oscillator
The quantum harmonic oscillator is the quantum-mechanical analog of the classical harmonic oscillator. Because an arbitrary smooth potential can usually be approximated as a harmonic potential at the vicinity of a stable equilibrium point, it is one of the most important model systems in quantum mechanics. Furthermore, it is one of the few quantum-mechanical systems for which an exact, analytical solution is known. One-dimensional harmonic oscillator Hamiltonian and energy eigenstates The Hamiltonian of the particle is: \hat H = \frac + \frac k ^2 = \frac + \frac m \omega^2 ^2 \, , where is the particle's mass, is the force constant, \omega = \sqrt is the angular frequency of the oscillator, \hat is the position operator (given by in the coordinate basis), and \hat is the momentum operator (given by \hat p = -i \hbar \, \partial / \partial x in the coordinate basis). The first term in the Hamiltonian represents the kinetic energy of the particle, and the second ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Harmonic Oscillator
In classical mechanics, a harmonic oscillator is a system that, when displaced from its equilibrium position, experiences a restoring force ''F'' proportional to the displacement ''x'': \vec F = -k \vec x, where ''k'' is a positive constant. The harmonic oscillator model is important in physics, because any mass subject to a force in stable equilibrium acts as a harmonic oscillator for small vibrations. Harmonic oscillators occur widely in nature and are exploited in many manmade devices, such as clocks and radio circuits. If ''F'' is the only force acting on the system, the system is called a simple harmonic oscillator, and it undergoes simple harmonic motion: sinusoidal oscillations about the equilibrium point, with a constant amplitude and a constant frequency (which does not depend on the amplitude). If a frictional force ( damping) proportional to the velocity is also present, the harmonic oscillator is described as a damped oscillator. Depending on the friction ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
LC Circuit
An LC circuit, also called a resonant circuit, tank circuit, or tuned circuit, is an electric circuit consisting of an inductor, represented by the letter L, and a capacitor, represented by the letter C, connected together. The circuit can act as an electrical resonator, an electrical analogue of a tuning fork, storing energy oscillating at the circuit's resonant frequency. LC circuits are used either for generating signals at a particular frequency, or picking out a signal at a particular frequency from a more complex signal; this function is called a bandpass filter. They are key components in many electronic devices, particularly radio equipment, used in circuits such as oscillators, filters, tuners and frequency mixers. An LC circuit is an idealized model since it assumes there is no dissipation of energy due to resistance. Any practical implementation of an LC circuit will always include loss resulting from small but non-zero resistance within the components and connect ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Impedance Of Free Space
In electromagnetism, the impedance of free space, , is a physical constant relating the magnitudes of the electric and magnetic fields of electromagnetic radiation travelling through free space. That is, Z_0 = \frac, where is the electric field strength, and is the magnetic field strength. Its presently accepted value is : , where Ω is the ohm, the SI unit of electrical resistance. The impedance of free space (that is, the wave impedance of a plane wave in free space) is equal to the product of the vacuum permeability and the speed of light in vacuum . Before 2019, the values of both these constants were taken to be exact (they were given in the definitions of the ampere and the metre respectively), and the value of the impedance of free space was therefore likewise taken to be exact. However, with the revision of the SI that came into force on 20 May 2019, the impedance of free space as expressed with an SI unit is subject to experimental measurement because only t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dielectric Constant
The relative permittivity (in older texts, dielectric constant) is the permittivity of a material expressed as a ratio with the electric permittivity of a vacuum. A dielectric is an insulating material, and the dielectric constant of an insulator measures the ability of the insulator to store electric energy in an electrical field. Permittivity is a material's property that affects the Coulomb force between two point charges in the material. Relative permittivity is the factor by which the electric field between the charges is decreased relative to vacuum. Likewise, relative permittivity is the ratio of the capacitance of a capacitor using that material as a dielectric, compared with a similar capacitor that has vacuum as its dielectric. Relative permittivity is also commonly known as the dielectric constant, a term still used but deprecated by standards organizations in engineering as well as in chemistry. Definition Relative permittivity is typically denoted as (som ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Compton Wavelength
The Compton wavelength is a quantum mechanical property of a particle, defined as the wavelength of a photon whose energy is the same as the rest energy of that particle (see mass–energy equivalence). It was introduced by Arthur Compton in 1923 in his explanation of the scattering of photons by electrons (a process known as Compton scattering). The standard Compton wavelength of a particle of mass is given by \lambda = \frac, where is the Planck constant and is the speed of light. The corresponding frequency is given by f = \frac, and the angular frequency is given by \omega = \frac. The CODATA value for the Compton wavelength of the electron is Other particles have different Compton wavelengths. Reduced Compton wavelength The reduced Compton wavelength \lambda\!\!\!\bar ( barred lambda) of a particle is defined as its Compton wavelength divided by : : \lambda\!\!\!\bar = \frac = \frac, where is the reduced Planck constant. Role in equations for massive pa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vacuum Permeability
The vacuum magnetic permeability (variously ''vacuum permeability'', ''permeability of free space'', ''permeability of vacuum'', ''magnetic constant'') is the magnetic permeability in a classical vacuum. It is a physical constant, conventionally written as ''μ''0 (pronounced "mu nought" or "mu zero"), approximately equal to 4π × 10−7 H/m (by the former definition of the ampere). It quantifies the strength of the magnetic field induced by an electric current. Expressed in terms of SI base units, it has the unit Kilogram, kg⋅Metre, m⋅Second, s−2⋅A−2. It can be also expressed in terms of SI derived units, Newton (unit), N⋅A−2, Henry (unit), H·m−1, or Tesla (unit), T·m·A−1, which are all equivalent. Since the 2019 revision of the SI, revision of the SI in 2019 (when the values of ''Elementary charge, e'' and ''Planck constant, h'' were fixed as defined quantities), ''μ''0 is an experimentally determined constant, its value being proportional ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Von Klitzing Constant
The quantum Hall effect (or integer quantum Hall effect) is a quantized version of the Hall effect which is observed in two-dimensional electron systems subjected to low temperatures and strong magnetic fields, in which the Hall resistance exhibits steps that take on the quantized values : R_ = \frac = \frac , where is the Hall voltage, is the channel current, is the elementary charge and is the Planck constant. The divisor can take on either integer () or fractional () values. Here, is roughly but not exactly equal to the filling factor of Landau levels. The quantum Hall effect is referred to as the integer or fractional quantum Hall effect depending on whether is an integer or fraction, respectively. The striking feature of the integer quantum Hall effect is the persistence of the quantization (i.e. the Hall plateau) as the electron density is varied. Since the electron density remains constant when the Fermi level is in a clean spectral gap, this situation corres ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fine-structure Constant
In physics, the fine-structure constant, also known as the Sommerfeld constant, commonly denoted by (the Alpha, Greek letter ''alpha''), is a Dimensionless physical constant, fundamental physical constant that quantifies the strength of the electromagnetic interaction between elementary charged particles. It is a dimensionless quantity (dimensionless physical constant), independent of the system of units used, which is related to the strength of the coupling of an elementary charge ''e'' with the electromagnetic field, by the formula . Its numerical value is approximately , with a relative uncertainty of The constant was named by Arnold Sommerfeld, who introduced it in 1916 Equation 12a, ''"rund 7·" (about ...)'' when extending the Bohr model of the atom. quantified the gap in the fine structure of the spectral lines of the hydrogen atom, which had been measured precisely by Albert A. Michelson, Michelson and Edward W. Morley, Morley in 1887. Why the constant should have t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
