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Free electron can move anywhere in nature Or Tendency of any electron to move in atmosphere


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Both concepts are mathematical in character and they ultimately describe the same characteristics or situations. "Invariance" is a more technical word because it says "what has to be equal to what" for us to say that the symmetry exists. In particular, the "invariance under a symmetry transformation" means that an object, like the action $S$, has the same ...


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To see why a wave must move, you must see how the wave equation is derived from the force field that causes it. Think of a wave on a stretched string. If there is a disturbance at one point, stretching the string there, the string tension will force the adjacent part of the string to stretch too, and so forth.


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All waves are superpositions of sine waves of various wavelengths. Since a sine wave in a uniform medium (one which does not allow reflection) goes on forever, so must a superposition of such waves, unless the waves in the superposition are chosen just right to make the sum cancel out beyond a certain distance. But it cannot drop to 0 immediately at the ...


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The magnitude of static friction adjust its value to the applied force hence static friction is called self adjustable....


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Just to add, nonlocal dielectric response also leads to the permittivity being dependent on the wavevector. Nonlocality is thus tightly bound to the notion of spatial dispersion. This has profound implications on the light propagation is nonlocal media. The dispersion curves can be bent upwards or downwards with the wavenumber. Therefore, it may occur that ...


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I found a paper that discusses this nonlocality in the context of intermolecular interactions. Not the same context as the article you linked, but it may help with understanding the concept. "The nonlocal dielectric function of a molecule determines the effective potential at a certain point due to an applied external potential at a different point, within ...


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It means polarization $\mathbf P$ at point $\mathbf x$ is an integral involving electric field $\mathbf E$ at points $\mathbf x'$ different from $\mathbf x$.


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The term 'amplitude' is often used somewhat ambiguously. The most rigorous definition is that amplitude is simply $|A|$ (the modulus of $A$). In your case (unmodulated wave or oscillation) there's only one amplitude. But others count the number of peaks and troughs as 'amplitudes' like you are doing. You count only three but that's because Fig.14.2 only ...


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In many cases people do seem to say "Fourier frequency" when they mean "frequency". However, when dealing with data defined only on discrete time points the phrase "Fourier frequency" has important meaning. Consider a sequence of $N$ values $\{ x_n \}$ where $n \in \{1, 2, \ldots N \}$. This situation comes up all the time if we have a physical signal ...


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See this wikipedia article. It is probable the "S" stands for Spanier as in Edwin Spanier.


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According to here, there was no precise definition before this group redefined what it meant for a group of galaxies to constitute a supercluster--before their redefinition, it seems it was just loosely defined as "extended regions with a high concentration of galaxies." They now define a supercluster to be a volume in which "the motions of galaxies are ...


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The states of charmonium are treated as bound states of a charmed quark ($c$) and its anti-quark ($\bar{c}$). Since the binding energy of the $c-\bar{c}$ system is relatively small, compared to the rest energy of the charmed quarks, it is a reasonable starting point to analyze the states using the non-relativistic Schroedinger equation with a potential ...


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Don't confuse theory with reality. Electromagnetic theory (i.e., the theory of Maxwell) talks about waves of electric and magnetic field strength. The standard model of particle physics talks about photons---discrete particles/packets of energy---whose appearance are governed by probability densities that obey wave-like laws. As far as we know, gamma rays ...


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Two different wave concepts are being confused here and called an EM wave. There exists electromagnetic radiation from light to radio waves to gamma rays , and for that see this answer of mine which explains how the classical wave of the Maxwell equations is an emergent phenomenon: it is built up by photons. And there exist the alternating currents in ...


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Every phase transition has an order parameter: something that vanishes above the transition temperature and is finite below. In superconductors, the order parameter is a complex quantity related to the superconducting gap: $\Delta = |\Delta| e^{i \phi}$. In BCS theory, there is a self-consistent equation for the gap: $\Delta_k = -\sum_q V_{kq} ...


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In condensed matter "bulk" does not refer to the dimensionality of the problem but the location in the material. It refers to the volume of the crystal, as opposed to, e.g., surface effects. Many organic conductors behave as 1D systems, yet you can talk about bulk properties. Copper oxide superconductors have a 2D physics. However, often you will find ...


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according to me a body is homogeneous when the properties that defines its physical structure are same at all points(or space) while a body is isotropic if the value of properties,that affect some physical phenomenon,is same in all directions


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When you push a rope, it has that bulk property to easily change its shape and bend without producing much of a reaction force. But if you pack the rope in a very narrow hollow cylinder (an impossible ideal case indeed) where the rope won't have the freedom to bend, and then push it, it will get compressed first filling up gaps in the fiber binding but after ...


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The metric tensor $g_{\mu\nu}$ in 4 dimensions has 10 independent components. Each of these has the potential of being a dynamical degree of freedom, also know as a "mode." There are many different ways of parameterizing these 10 components. In general, of the 10 components, you can always pick one of them to correspond to the overall local scale of the ...


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We have the surface charge density as charge/area. Now consider


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A proto-stellar disk is composed of gas and dust from a giant molecular dust cloud that collapses into itself because of gravitational attraction. It's an early stage in the formation of a star. The collapse may be triggered by shock waves passing through the molecular cloud which disrupt the balance between inward gravitation and outward gas pressure that ...


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A circumstellar disk is a set of objects that orbit about a star-like object and that collectively look disk-like in some way. A protostellar disk is thus a kind of circumstellar disk, the asteroid belt and the Kuiper belt about our Sun are also circumstellar disks.


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Spin-resolved current in the context of scanning probe methods means that due to a finite magnetisation of probe and sample the current consists of electrons of one spin in a larger quantity than of the other. Spin current usually refers to current that consists exclusively of electrons of one spin direction.


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Hopefully, I will not be "bad mouthing" those who have a background similar to my own, but here goes. In the world of chemical engineering, there are quite a few equations that are much more empirical than "first principle" based. This is particularly true for heat transfer problems, which usually have to deal with turbulent fluids. From a practical ...


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Field emission and field electron emission are the terms. From wikipedia: The terminology is historical because related phenomena of surface photoeffect, thermionic emission (or Richardson–Dushman effect) and "cold electronic emission", i.e. the emission of electrons in strong static (or quasi-static) electric fields, were discovered and studied ...


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When it is saying the light rays converge, it means that they intersect. THe light rays intersect because the lens bends them so they all point at the same spot. I will explain more. When a point source emits light, it emits in all directions. This is why if you are in a dark room and you put a candle in front of a sheet of paper, you will see a diffuse ...


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Wavelength and wavenumber are redundant terms, as it sounds like you know. Their use is a matter of convention, which in my experience changes from field to field which you won't know until you've been around. So...if you know which one people use, go with the flow. Otherwise, use which one you know, and be confident; for questions of order-of-magnitude ...


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I don't think there's much to say beyond the obvious: You should use whatever terminology is most helpful in communicating the information that you want to communicate. That has to do with the audience you're talking to. Just like how you use °F when talking to Americans and °C when talking to non-Americans ... similarly it's often wise to use cm^-1 when ...


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Traditionally wavenumber is used in molecule spectrums such as infrared spectrums in organic chemistry where it is given in the incoherent SI-unit $\textrm{cm}^{-1}$. Mostly because one obtains convenient numbers on the axis. Also in most of the wave equations it is used, because again you can make the convenient substitution $k \equiv \frac{2\pi}{\lambda} = ...



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