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Unitary Transformation (quantum Mechanics)
In quantum mechanics, the Schrödinger equation describes how a system changes with time. It does this by relating changes in the state of the system to the energy in the system (given by an operator called the Hamiltonian (quantum mechanics), Hamiltonian). Therefore, once the Hamiltonian is known, the time dynamics are in principle known. All that remains is to plug the Hamiltonian into the Schrödinger equation and solve for the system state as a function of time. Often, however, the Schrödinger equation is difficult to solve (Numerical methods for ordinary differential equations, even with a computer). Therefore, physicists have developed mathematical techniques to simplify these problems and clarify what is happening physically. One such technique is to apply a unitary transformation to the Hamiltonian. Doing so can result in a simplified version of the Schrödinger equation which nonetheless has the same solution as the original. Transformation A unitary transformation (or ... [...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] |
Driven Harmonic Motion
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 coeff ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Beam Splitter
A beam splitter or beamsplitter is an optical instrument, optical device that splits a beam of light into a transmitted and a reflected beam. It is a crucial part of many optical experimental and measurement systems, such as Interferometry, interferometers, also finding widespread application in fibre optic telecommunications. Designs In its most common form, a cube, a beam splitter is made from two triangular glass prism (optics), prisms which are glued together at their base using polyester, epoxy, or urethane-based adhesives. (Before these synthetic resins, natural ones were used, e.g. Canada balsam.) The thickness of the resin layer is adjusted such that (for a certain wavelength) half of the light incident through one "port" (i.e., face of the cube) is reflection (physics), reflected and the other half is transmitted due to Total internal reflection#Frustrated_TIR, FTIR (frustrated total internal reflection). polarizer, Polarizing beam splitters, such as the Wollaston prism ... [...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] |
Qubit Offresonant
In quantum computing, a qubit () or quantum bit is a basic unit of quantum information—the quantum version of the classic binary bit physically realized with a two-state device. A qubit is a two-state (or two-level) quantum-mechanical system, one of the simplest quantum systems displaying the peculiarity of quantum mechanics. Examples include the spin of the electron in which the two levels can be taken as spin up and spin down; or the polarization of a single photon in which the two spin states (left-handed and the right-handed circular polarization) can also be measured as horizontal and vertical linear polarization. In a classical system, a bit would have to be in one state or the other. However, quantum mechanics allows the qubit to be in a coherent superposition of multiple states simultaneously, a property that is fundamental to quantum mechanics and quantum computing. Etymology The coining of the term ''qubit'' is attributed to Benjamin Schumacher. In the acknowledgment ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lab Offresonant
Lab most often refers to: * Laboratory, a facility to conduct scientific research and experiments. Lab or LAB may also refer to: Places * Láb, a village near Br in western Slovakia * Lab a school in Chicago Music * LAB Records, a British independent record label * LAB (band), a Finnish band * L.A.B., a New Zealand reggae band Transportation * Laburnum railway station, Melbourne * League of American Bicyclists * Linhas Aéreas Brasileiras, a defunct Brazilian airline * Lloyd Aéreo Boliviano, a defunct Bolivian airline Science and technology * Linear alkylbenzene * Lithosphere-Asthenosphere boundary, between layers of the Earth * Lactic acid bacteria * Lab color space * Lyman-alpha blob, in interstellar space * Linear alkylbenzene sulfonate Groups * Langile Abertzaleen Batzordeak, a Basque trade union * Lockerz advisory board * Los Angeles Baptist High School, US Other * Labrador Retriever, a dog breed * Legs, abs, and butt fitness workout See also * Labs (disambigua ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Qubit Resonant
In quantum computing, a qubit () or quantum bit is a basic unit of quantum information—the quantum version of the classic binary bit physically realized with a two-state device. A qubit is a two-state (or two-level) quantum-mechanical system, one of the simplest quantum systems displaying the peculiarity of quantum mechanics. Examples include the spin of the electron in which the two levels can be taken as spin up and spin down; or the polarization of a single photon in which the two spin states (left-handed and the right-handed circular polarization) can also be measured as horizontal and vertical linear polarization. In a classical system, a bit would have to be in one state or the other. However, quantum mechanics allows the qubit to be in a coherent superposition of multiple states simultaneously, a property that is fundamental to quantum mechanics and quantum computing. Etymology The coining of the term ''qubit'' is attributed to Benjamin Schumacher. In the acknowledgment ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Resonant Lab
Resonance is a phenomenon that occurs when an object or system is subjected to an external force or vibration whose frequency matches a resonant frequency (or resonance frequency) of the system, defined as a frequency that generates a maximum amplitude response in the system. When this happens, the object or system absorbs energy from the external force and starts vibrating with a larger amplitude. Resonance can occur in various systems, such as mechanical, electrical, or acoustic systems, and it is often desirable in certain applications, such as musical instruments or radio receivers. However, resonance can also be detrimental, leading to excessive vibrations or even structural failure in some cases. All systems, including molecular systems and particles, tend to vibrate at a natural frequency depending upon their structure; when there is very little damping this frequency is approximately equal to, but slightly above, the resonant frequency. When an oscillating force, an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rotating Wave Approximation
The rotating-wave approximation is an approximation used in atom optics and magnetic resonance. In this approximation, terms in a Hamiltonian that oscillate rapidly are neglected. This is a valid approximation when the applied electromagnetic radiation is near resonance with an atomic transition, and the intensity is low. Explicitly, terms in the Hamiltonians that oscillate with frequencies \omega_L + \omega_0 are neglected, while terms that oscillate with frequencies \omega_L - \omega_0 are kept, where \omega_L is the light frequency, and \omega_0 is a transition frequency. The name of the approximation stems from the form of the Hamiltonian in the interaction picture, as shown below. By switching to this picture the evolution of an atom due to the corresponding atomic Hamiltonian is absorbed into the system ket, leaving only the evolution due to the interaction of the atom with the light field to consider. It is in this picture that the rapidly oscillating terms mentioned prev ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Oscillation
Oscillation is the repetitive or periodic variation, typically in time, of some measure about a central value (often a point of equilibrium) or between two or more different states. Familiar examples of oscillation include a swinging pendulum and alternating current. Oscillations can be used in physics to approximate complex interactions, such as those between atoms. Oscillations occur not only in mechanical systems but also in dynamic systems in virtually every area of science: for example the beating of the human heart (for circulation), business cycles in economics, predator–prey population cycles in ecology, geothermal geysers in geology, vibration of strings in guitar and other string instruments, periodic firing of nerve cells in the brain, and the periodic swelling of Cepheid variable stars in astronomy. The term ''vibration'' is precisely used to describe a mechanical oscillation. Oscillation, especially rapid oscillation, may be an undesirable phenomenon in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Resonance
Resonance is a phenomenon that occurs when an object or system is subjected to an external force or vibration whose frequency matches a resonant frequency (or resonance frequency) of the system, defined as a frequency that generates a maximum amplitude response in the system. When this happens, the object or system absorbs energy from the external force and starts vibrating with a larger amplitude. Resonance can occur in various systems, such as mechanical, electrical, or acoustic systems, and it is often desirable in certain applications, such as musical instruments or radio receivers. However, resonance can also be detrimental, leading to excessive vibrations or even structural failure in some cases. All systems, including molecular systems and particles, tend to vibrate at a natural frequency depending upon their structure; when there is very little damping this frequency is approximately equal to, but slightly above, the resonant frequency. When an Oscillation, oscillat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rotating Reference Frame
A rotating frame of reference is a special case of a non-inertial reference frame that is rotation, rotating relative to an inertial reference frame. An everyday example of a rotating reference frame is the surface of the Earth. (This article considers only frames rotating about a fixed axis. For more general rotations, see Euler angles#Vehicles and moving frames, Euler angles.) Fictitious forces All non-inertial reference frames exhibit fictitious forces; rotating reference frames are characterized by three: * the centrifugal force (fictitious), centrifugal force, * the Coriolis force, and, for non-uniformly rotating reference frames, * the Euler force. Scientists in a rotating box can measure the rotation speed and axis of rotation by measuring these fictitious forces. For example, Léon Foucault was able to show the Coriolis force that results from Earth's rotation using the Foucault pendulum. If Earth were to rotate many times faster, these fictitious forces could be fel ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
