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1

I am not sure if I've understood your question, but I'm gonna try to show off some light on this. Read it slowly and carefully, it needs a bit concentration and abstract thinking. Let's imagine that you integrate over a body, summing infinite infinitessimal partitions of this body over its volume. i.e. $\int_v dV$ as you well know. But, what that means? Let ...


3

The idea behind the notation is that the operator $F$ is supposed to count the number of fermions in an expression, i.e. $$[F,A_n]= n A_n$$ if the operator $A_n$ contains $n$ fermions, what that means. Then $$[f(F),A_n]= f(n) A_n$$ for a sufficiently well-behaved function $f:\mathbb{C}\to \mathbb{C}$. In particular, for $f(x)=(-1)^x $, one has ...


2

The (Lie-)group $U(1)$ is the topological space $S^1$ (what we call a circle together with its standard open subsets) together with a rule how to multiply its points. In its representation as numbers in ${\mathbb C}$ with absolute value $1$, we have ${\mathrm e}^{{\mathrm i}\alpha}\bullet{\mathrm e}^{{\mathrm i}\beta}:={\mathrm e}^{{\mathrm ...


2

Engineers created that problem. ;) (probably not) Many physics books use $Y$ for Young's modulus (Symon, Knight, Young & Freedman). Taylor's Classical Mechanics uses YM. Halliday, Resnick & -fill-in-the-blank- state that engineers use $E$. I suspect that physicists started using $Y$ for exactly this reason: to highlight a difference in the meanings ...


0

Coincidence, nothing deep I'd say. Note that the equation representing the electric field modulus depends on the units you've picked and as such putting so much emphasis on the exact characters appearing in the eq. is senseless. Note that it's possible to form many physics equalities and equations involving 3 characters. E, epsilon and sigma are quite used. ...


2

Yeah, that's just a coincidence. The easy way to see this is that $\epsilon$ is a relatively static property of a dielectric but a totally dynamic property of a stretching material.


4

Just a coincidence. There are too many quantities and not enough letters. It probably does make a difference that the fields in which these two equations exist (material science and electromagnetism) are well enough separated that you typically won't see them both in the same papers or textbooks; if that weren't the case, people would start using different ...


3

No. The $p_x$ and $p_y$ orbitals are always real-valued, and the complex-valued $|m|=1$ orbitals are always denoted $p_{1}$ and $p_{-1}$. Depending on what scheme you're using, the third $l=1$ orbital can be denoted either $p_z$ or $p_0$, with both notations completely equivalent. Just because the $p_x$ and $p_y$ orbitals are linear combinations of $p_1$ ...


2

You have stumbled upon a difference between how chemists and physicist denote orbitals. The $p_x, p_y, p_z$ notation is common in chemistry because the resulting orbitals are real. Physicist use $p_{-1}, p_0, p_1$ where the subscripts are the values of m and embrace the complexity of the resulting wave function. It is purely a matter of choice since all ...


0

The point is that luminous intensity is intensity as perceived by the human eye, and particularly taking into account the fact that the same amount of power will be perceived as brighter or dimmer depending on whether the wavelength is at a maximum of the eye's sensibility or at a minimum. This makes the candela ever so slightly washier than the other six ...


0

Personally, from a pure physics point of view, i don't think we need the candela as a base S.I. unit. it seems that all we need is: m,kg,s,A,K,mol These can all be related to basic physics constants (see Physics Today, July 2014, p. 37): c,h,delta nu(pick any atomic transition),e,k(Boltzmann),N_A(Avogadro's) Actually, even N_A is only necessary from a ...


3

This notation is mostly used in astronomy (or at least I haven't seen it elsewhere), and it is used to de-dimensionalize variables, or otherwise get rid of inconvenient units and exponents, whilst keeping track of what standard each variable is measured in. This is not really a unified notation; instead, it is a bunch of different variables the author have ...


0

There are definite advantages of differential forms, geometric calculus, and four vectors over 3d Gibbs vector algebra and vector calculus. Specifically you can solve for the electromagnetic field first ... and then let someone break it into electric and magnetic parts later if they feel like it (if at all). For instance the field due to a non accelerating ...


1

Here's a paper for you to ponder on: Teaching electromagnetic field theory using differential forms Excerpt from the abstract: computational simplifications result from the use of forms: derivatives are easier to employ in curvilinear coordinates, integration becomes more straightforward, and families of vector identities are replaced by ...


0

A state $|\psi\rangle$ in quantum mechanics is a piece of information about a system that can be copied. $|\psi\rangle\langle\psi|$ and $\langle\psi|$ are both best understood as alternate representations of that same state. And $\langle\psi|\psi\rangle$ is a complex number such that $|\langle\psi|\psi\rangle|^2$ is the probability of the state ...


3

I think the easiest way to think about these objects is as follows: $|\psi\rangle$ is your physical state Your physical state comes with a machine (its dual) $\langle \psi |$, which when applied to any other physical state $|\phi \rangle$, spits out the overlap $\langle \psi | \phi \rangle$ between your state and $|\phi\rangle$ It also comes with a ...


3

We can talk about what the notation represents. Terms I introduce will be italicised. For 1, the ket $\left|\psi\right\rangle$ represents the state of a physical system. Quantum mechanics claims these are elements of a vector space. So far, it's all physical. However, everything afterwards will abstract from that. For 2 and 4, the bra ...


5

These states represent intermediate coupling schemes that are halfway between the usual $LS$ coupling and the more extreme $jj$ coupling that happens in heavier atoms where relativistic effects mean that the spin-orbit coupling for each individual electron can match or exceed the orbit-orbit coupling between different electrons. The intermediate coupling ...


0

It appears that none of Physical Review Style and Notation Guide, the AIP Style Manual, the IAU Style Manual, or The ACS Style Guide: A Manual for Authors and Editors, weigh in at all on this matter, so I would say it is to some extent up to personal taste. Some recent examples from the literature: $6356 ± 8 \:\mathrm{keV}$ $75.3a_0^3 ± 0.4a_0^3$ ...


1

It seems to me that there should be a mistake. Let $A^{\mu}(x)=\partial^{\mu} \theta (x)$. Clearly you have $F^{\mu \nu}=0$. Thus, you just have to find a function $\theta(x)$ such that: $$(\partial_{\nu} \partial_{\mu} \theta)(\partial^{\nu} \partial^{\mu} \theta)\neq \frac{1}{2} (\partial_{\nu} \partial^{\nu} \theta)(\partial_{\mu} \partial^{\mu} \theta). ...


2

Horizontal position of indices matters in principle because one might want to raise and lower indices on the Christoffel symbols. If the horizontal position of indices are not observed in a consistent manner, it becomes ambiguous which index was raised or lowered, and so forth, in particular if the connection is not torsionfree. Also note that different ...



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