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8

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 ...


6

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 ...


5

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.


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


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. ...


3

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.


3

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 ...


2

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 $10^{-1}mm$.


2

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 ...


2

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 ...


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.


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 ...


1

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).


1

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 ...


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 $GaAs$/$AlAs$ ...


1

Diffeomorphism Invariance Let $M$ be a smooth manifold. Let $\phi: M \to M$ be a diffeomorphism. A simple property of the Einstein equations is $$ g \in \otimes^2 TM \text{ is solution to vacuum Einstein equation} \implies \text{ so is } \phi^*g $$ To see that this is true, simply pull back both sides of the Einstein equation by $\phi$, and use the ...



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