# Tag Info

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Scattering is phenomenon of deviation from its trajectory due to non-uniformities in medium through which it is passing. Eg. When a ball is deviated by tennis bat due to its motion. Flourescnce is consuming the photon, and emitting back lower energy photon.

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Like Wikipedia says: "Moment is a combination of a physical quantity and a distance." This 'physical quantity' could be various things. To take the examples you mention: Moment of momentum (commonly known as angular momentum) is expressed as $\vec{L}=\vec{r}\times m\vec{v}$, and is a measure for the rotational momentum of an object around some axis. Moment ...

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A Hilbert space $\cal H$ is complete which means that every Cauchy sequence of vectors admits a limit in the space itself. Under this hypothesis there exist Hilbert bases also known as complete orthonormal systems of vectors in $\cal H$. A set of vectors $\{\psi_i\}_{i\in I}\subset \cal H$ is called an orthonormal system if $\langle \psi_i |\psi_j \rangle ... 3 This completeness relation of the basis means that you can reach all possible directions in the Hilbert space. It means that any$|\psi \rangle$can be made up from these basis vectors. If the sum of the projectors (the ket-bras) would not be the unit matrix, the vector$|\psi\rangle$could have components which cannot be represented within your basis. ... 1 A compositional superlattice is a periodic layer structure of different materials. These typically have different bandgaps, effective masses, refractive indices etc. There are limitations on which materials can be stacked. They need to have the same crystal structure and lattice constant or at least negligible strain. The model system would be$GaAs$/$AlAs$... 3 These are conjugate variables. 4 Your issue is that this interview was not transcribed by a physicist! What he said was "Gauge Symmetry" not "Gate Symmetry". Your googling should work better now, and here is one place to start: https://en.wikipedia.org/wiki/Gauge_theory 0 In both cases, the speed of the body at time$t=0$would be zero, if it was initially at rest. Then you will ask, what is the difference between an impulsive force and an "ordinary force" which keeps acting continuously? Actually, there is no fundamental difference between them. But when we say impulsive force, we mean that the force is of very large ... 0 In case of a travelling observer , there is change in wavelength,and the magnitude and sign of change in wavelength depends on the velocity of the observer. Let's say an observer moves towards a stationary source emitting pulses with a frequency of 'f' with a velocity vo . A pulse reaches the observer and by the next time a pulse reaches the observer, the ... 2 It's a LaTeX typo. The author meant to write$\mathbf{r}$, i.e. '\bf{r}' where they've defined \bf as a macro for \mathbf. They forgot the slash. 0 The answers already given explain the differences between the processes by which heat is transferred from one body to another but there are also differences in their relative importance in particular situations. A central heating radiator does radiate heat but convection is a more important process once the air is heated and before that conduction through ... 1 I would assume that to mean the zeroth component of the energy-momentum four-vector, for which$p^\mu p_\mu=-m^2$is an expression of the full version of the famous mass-energy equivalence formula (plus or minus, depending on a sign convention you can choose).$p^\mu p_\mu$is Einstein notation for, in this case,$p^\mu p_\mu=\frac{1}{c^2}E^2 ...

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If a constraint can be expressed as f(r1,r2,...t) =0 . position vectors are connected with time then the constraints are called holonomic ,but if they can not be expressed as above then the constraints are non-holonomic

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I don't think there is a really strict definition of a ray. I would say that a reasonable definition is: electromagnetic energy density is confined to a finite area (e.g. gauss beam and not plane wave) in the transversal plane The Poynting vectors are reasonably parallel in this plane. (e.g. gauss beam and not spherical wave) The direction the ray moves ...

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I just found this source (1) which explains that rays are curves such that the direction a ray points is the same as that of the Poynting vector at a given point. References (1) p110 of 'Microwave Antenna Theory and Design' by S.Silver (link to google books)

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Regular functions are well defined (finite). Irregular functions tend to infinity in the limit of approaching some point. In this case, all the Bessel functions tend to zero (except j0 which goes to 1) as you approach the origin. The Neumann functions approach +infinity as you approach the origin from the positive side.

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I will talk about $SU(3) \times SU(2)$. First, a matrix $T_3 \in SU(3)$ acts in the fundamental representation on $\mathbb C^3$ in the following way: A vector $\vec v \in \mathbb C^3$ with components $v_i$ is mapped to $v'_i = (T_3)_{ij} v_j$. Similarly, a $T_2 \in SU(2)$ acts on $\vec w \in \mathbb C^2$ as $w'k = (T_2)_{kl} w_l$. The bifundamental ...

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A distributed normal force acting on a body due to contact with another body may be represented by a single normal force acting at the centre of action of the distributed force, but may just as validly be represented by a force-torque pair - i.e. by a force acting at a point on the surface, and a torque. In the latter situation, the force is a "normal ...

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You're close. In some very general way we could start with definitions: Interferometry You use a constant and well understood light and vary some parameter of the light's paths through the machine (either by changing the length of a leg, changing the material on one leg, or changing the motion of the material on one leg. To repeat: hold the light steady ...

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There is no randomness in quantum mechanics, there is only uncertainty. , as stated, whoever may have said it. Mathematical definition of randomness: The fields of mathematics, probability, and statistics use formal definitions of randomness. In statistics, a random variable is an assignment of a numerical value to each possible outcome of an event ...

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I had a little research on it. First of all, Quantum Mechanics is all based on probabilities. What is a probability. It gives you the chance for a specific event to occur from a list of possible events. Now what is the probability of a probability. Suppose if you say that there is 80% probability of finding a particle, there is a most possible chance for ...

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The core of your question is subtle, so I'll be careful in how I set up my answer. In my understanding of quantum mechanics, wave function collapse is the closest a physical process can be to the mathematical idealization of a random variable. However, before the collapse, a complicated many-body process, the wave function evolution of the system is ...

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Randomness is a behavior that is unpredictable and there can be no mathematical pattern to it. However, uncertainty does have a mathematical pattern, thus proving randomness as false. For instance, you can scribble all over a piece of paper and you can eventually find some mathematical pattern even though what you've done seemed like it was pure ...

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Wow: this is a very good question - and the answers all miss the most interesting point! :) That's a good observation, there is no precise definition of where a cycle ends if you have some change in the amplitude. But do not be sad about it, take it positive: this explains (well, it's at least a very good analogy) the uncertainty principle. In QM particles ...

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This is mainly a matter of definition, a damped oscillation is not periodic, since it dies away, that's why you cannot really talk about "period" or "cycle" in the usual way. What I've seen is definitions of "pseudo-period" and "pseudo-cycle" when one talks about the analogous concepts in damped oscillations.

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To understand the phase matching concept I recommend you to do the calculus of the wave equation as explained in Boyd's book (Nonlinear optics - The wave equation for nonlinear optical media). You might also find them in every nonlinear optics course but I think they are well explained in Boyd's book. Phase matching in general is used meaning momentum ...

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Yeah, @EddyKhemiri, as @almagest wrote it isn't just visible light, but rather that all electromagnetic waves moving through a vacuum travel at $c$. Also- just a pet peeve, but remember that this is the speed in a vacuum; it can be slower in different mediums.

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Refraction occurs when a large number of dipoles scatter coherently. Each individual dipole scatters light in response to the incident radiation in (almost) all directions, but when you have a large collection of scatterers, each one scattering in many directions, you have to sum the contributions of each one in order to arrive at the total field. Each ...

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Generally speaking, the first and main difference is that refraction happen upon transmission of the light, while scattering happen upon reflection of the light (namely, diffusive reflection, where the angle of reflection does not equal to the angle of incident).

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Configuration space = manifold of allowed position configurations. It is the same for classical mechanics and quantum mechanics; for $n$ distinguishable particles, $R^{3n}$ minus the set of coordinates where two particles occupy the same position. State space = manifold of pure states of the system = manifold on which a deterministic dynamics is valid. Thus ...

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If you want to use SI nomenclature, that the following is acceptable: $0.1 mm = 0.1 mm (!), 100 \mu m = 100 000 nm ...$. How you wish to record it is up to you, though problem dependent. For example, you could record a $9 V$ battery as $9 000 mV, 9 000 000 \mu V, ...$.

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I have never seen anything like tmm or dmm... If it exists at all, it is highly non-standard. As others have mentioned in the comments, go with 0.1 mm or 100$\mu$m. I think that the conventional way of writing is $10^{-1}mm$.

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You can also use micrometer, and write $100\mu m$.

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Sometimes word usage is well-standardized, for example the words work and heat are well defined. Sometimes it is not, and one must be careful to understand what is meant by context. I don't believe that Schottky Barrier is as well standardized as work, but I think it's usage leans strongly toward the classic metal/semiconductor interface. I suppose it ...

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The division is conventionally made at the boundary between where stars end their lives as white dwarf stars and where more massive stars will end their lives in core collapse supernovae. The boundary is set both empirically, by observations of white dwarfs in star clusters, where their initial masses can be estimated, and also using theoretical models. ...

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The limit you quote seems to be a convention >massive star A star whose mass is larger than approximately 10 → solar masses. The → spectral types of massive stars range from about B3 (→ B star) to O2 (→ O star) and include → Wolf-Rayet stars as well as → Luminous Blue Variables and here: Massive stars are brighter, fuse faster, and perish more ...

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