Questions tagged [notation]

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67
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10answers
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Should zero be followed by units? [duplicate]

Today at a teachers' seminar, one of the teachers asked for fun whether zero should be followed by units (e.g. 0 metres/second or 0 metre or 0 moles). This question became a hot topic, and some ...
47
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3answers
10k views

Mathematically-oriented Treatment of General Relativity

Can someone suggest a textbook that treats general relativity from a rigorous mathematical perspective? Ideally, such a book would Prove all theorems used. Use modern "mathematical notation" as ...
39
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4answers
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Can units be plural? [duplicate]

I was in a conversation with my senior engineer where he kept on insisting that we can use plural when we write down any unit. I argued that it is not the 'common' practice or even throughout my whole ...
37
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8answers
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Is it foolish to distinguish between covariant and contravariant vectors?

A vector space is a set whose elements satisfy certain axioms. Now there are physical entities that satisfy these properties, which may not be arrows. A co-ordinate transformation is linear map from a ...
36
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2answers
39k views

Difference between $\Delta$, $d$ and $\delta$

I have read the thread regarding 'the difference between the operators $\delta$ and $d$', but it does not answer my question. I am confused about the notation for change in Physics. In Mathematics, $\...
35
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9answers
8k views

Why ket and bra notation?

So, I've been trying to teach myself about quantum computing, and I found a great YouTube series called Quantum Computing for the Determined. However. Why do we use ket/bra notation? Normal vector ...
32
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8answers
23k views

Is there a symbol for “unitless”?

I'm making a table where columns are labelled with the property and the units it's measured in: Length (m) |||| Force (N) |||| Safety Factor (unitless) ||| etc... I'd like not to write "unitless" ...
32
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2answers
19k views

Square bracket notation for dimensions and units: usage and conventions

One of the most useful tools in dimensional analysis is the use of square brackets around some physical quantity $q$ to denote its dimension as $$[q].$$ However, the precise meaning of this symbol ...
29
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2answers
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How to “decipher” the symbol for the recently announced doubly-charmed baryon?

The name of the particle (resonance?) in the recent announcement Observation of the doubly charmed baryon $\Xi^{++}_{cc}$ is complicated. I'm sure it's standard notation but I don't know how to "...
28
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2answers
2k views

Symbols of derivatives

What is the exact use of the symbols $\partial$, $\delta$ and $\mathrm{d}$ in derivatives in physics? How are they different and when are they used? It would be nice to get that settled once and for ...
23
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5answers
6k views

Is there a rigorous definition of 'much greater than'?

I have encountered $\gg$ in many physics text books where it's used as a relation between constants or functions but in none of the text books I have read is it properly defined anywhere. If $A \gg ...
19
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3answers
11k views

Derivative with respect to a vector is a gradient?

I've encountered in some books (and even completed an exercise from the Goldstein by using it), a strange notation that seems to work exactly like a gradient, I have tried to look for an explanation ...
18
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4answers
4k views

What does Peter Parkers formula represent?

Okay, so the trailer for the new Spider Man movie is out and appearently our friendly physicist from the neightborhood came up with something. However I can't find out what this is. Transcription: $...
17
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3answers
77k views

What does an integral symbol with a circle mean?

I have frequently seen this symbol used in advanced books in physics: $$\oint$$ What does the circle over the integral symbol mean? What kind of integral does it denote?
16
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4answers
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Why is the candela a base unit of the SI?

The candela is defined as The candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency $540\cdot10^{12}$ hertz and that has a radiant ...
15
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2answers
3k views

Tensor product in quantum mechanics?

I often see many-body systems in QM represented in terms of a tensor products of the individual wave functions. Like, given two wave functions with basis vectors $|A\rangle$ and $|B\rangle$, belonging ...
15
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1answer
3k views

Meaning of an image on Feynman's shirt

Is there any physical meaning of the image on Feynman's T-shirt?
15
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2answers
415 views

Searching books and papers with equations

Sometimes I may come up with an equation in mind, so I want to search for the related material. It may be the case that I learn it before but forget the name, or, there is no name for the equation yet....
14
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4answers
9k views

Difficulties with bra-ket notation

I have started to study quantum mechanics. I know linear algebra,functional analysis, calculus, and so on, but at this moment I have a problem in Dirac bra-ket formalism. Namely, I have problem with "...
14
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4answers
2k views

Hamilton equations from Poisson bracket's formulation

Referring to Wikipedia we have that the equation of motion for a $f(q, p, t)$ comes from the formula \begin{equation} \frac{\mathrm{d}}{\mathrm{d}t} f(p, q, t) = \frac{\partial f}{\partial q} \frac{\...
14
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2answers
12k views

Uncertainty in parenthesis

In a physics text book I read the following: $$e/m=1.758820150(44) ×10^{11} \mathrm{C/kg} $$ In this expression, $(44)$ indicates the likely uncertainty in the last two digits, $50$. How should ...
14
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3answers
2k views

Dirac Delta and Sloppy Notation

I am an undergraduate neuroscientist and recently I have been studying probability distributions in relation to information theory, and came across the definition of the Dirac Delta as a singular ...
13
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3answers
2k views

Having some issue with notation in a Hilbert space

What is the difference between these two? $\langle x|x\rangle$ and $|x\rangle\langle x|$ Are they the same? If they're the same, why are they used in these two different forms?
13
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4answers
3k views

Are covariant vectors representable as row vectors and contravariant as column vectors

I would like to know what are the range of validity of the following statement: Covariant vectors are representable as row vectors. Contravariant vectors are representable as column vectors. For ...
13
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2answers
9k views

Do derivatives of operators act on the operator itself or are they “added to the tail” of operators?

How do derivatives of operators work? Do they act on the terms in the derivative or do they just get "added to the tail"? Is there a conceptual way to understand this? For example: say you had the ...
12
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5answers
3k views

What exactly is $\hat{\psi}^\dagger(x)$? An operator or a function?

I've recently read Cohen-Tannoudji on quantum mechanics to try to better understand Dirac notation. A homework problem is giving me some trouble though. I'm unsure if I've learned enough yet to ...
12
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3answers
2k views

Matrices in Dirac Notation

I am in an undergraduate quantum mechanics course, and we are starting to use Dirac notation. I am a tad confused on exactly how all this works. Having taken linear algebra, I am very comfortable ...
11
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3answers
1k views

Why is the $dx$ right next to the integral sign in QFT literature?

I've noticed that in QFT literature, integrals are usually written as $\int \!dx ~f(x)$ instead of $\int f(x) dx$. Why?
11
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4answers
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How to indicate that a unit is dimensionless [duplicate]

For my dissertation I am preparing a list of symbols used in the text, which basically is a table that consists of the symbol, a short explanation and the dimension it has as indicated below: ...
11
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1answer
838 views

How are the definitions of a coherent state equivalent?

I am trying to understand coherent states. As far as I could find there are three equivalent definitions and in general many sources start from a different one, still I fail to see their equivalence. ...
11
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1answer
308 views

Group notation $\otimes$ and $\oplus$ used for representations of quarks and mesons

I've been trying to figure out this statement from the PDG quark model summary (PDF). Following $\mathrm{SU}(3)$, the nine possible $q\bar{q}′$ combinations containing the light $u$, $d$, and $s$ ...
11
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2answers
2k views

Historical reason behind using $ν$ instead of $f$ to stand for frequency in the equation $E=hν$?

Normally, we use the letter $f$ to stand for frequency in equations. $$T = 1/f$$ $$v = \lambda f$$ $$Φ +E_k = h f$$ So I'm curious as why the letter $ν$ (nu) is used to represent frequency in the ...
10
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2answers
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Advantages of using bra-ket notation [closed]

I’m curious whether people use bra-ket notation in QM for any reasons beyond convention. Are there any advantages to using bra-ket notation over ordinary linear algebraic notation? Are certain ...
10
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1answer
450 views

Is Schwarzschild's solution in his original paper consistent with current solutions? [duplicate]

I was reading the Schwarzschild's original paper where he derives the Schwarzschild metric for the first time(The english translated version found in arXiv : On the Gravitational Field of a Mass ...
10
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3answers
326 views

If the candela is a base SI unit, why isn't the sone an SI unit at all?

Related: Why is the candela a base unit of the SI? In the answers given in the previous question, the candela is included because lighting is important for humans. By the same argument, hearing is ...
9
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3answers
1k views

Why do some people write the gravitational force as proportional to $\mathbf{r}/|\mathbf{r}|^3$?

I'm reading Mathematical Aspects of Classical and Celestial Mechanics, Second Edition by Arnold, Kozlov, and Neishtadt. It occurred to me that many people like to use third power when mention the law ...
9
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4answers
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How does a linear operator act on a bra?

I'm studying QM from Shankar. He introduces linear operators and says that an operator is an instruction for transforming one ket into another. But then a few lines below he says operators can also ...
9
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1answer
310 views

What do term symbols with a half-integer “$L$” like $^3[3/2]_{1/2}$ mean?

Atomic term symbols are used to notate the angular momentum content of the electronic states of an atom, and are normally written down as $$^{2S+1}L_J$$ where the state has total spin $S$, spin ...
9
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3answers
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Staggered Indices ($\Lambda^\mu{}_\nu$ vs. $\Lambda_\mu{}^\nu$) on Lorentz Transformations

I have some open-ended questions on the use of staggered indices in writing Lorentz transformations and their inverses and transposes. What are the respective meanings of $\Lambda^\mu{}_\nu$ as ...
9
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2answers
673 views

Why distinguish between row and column vectors?

Mathematically, a vector is an element of a vector space. Sometimes, it's just an n-tuple $(a,b,c)$. In physics, one often demands that the tuple has certain transformation properties to be called a ...
8
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3answers
2k views

Is there a physical or mathematical symbol for “happens when”?

How would you denote symbolically, "Equilibrium happens given that ..."?
8
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5answers
2k views

Is 'amp' a technically invalid term?

I've been told to use the term ampere in exams and class (I'm in high school), instead of amp as it's not a valid unit, although I've been using the amp for years along with all of my friends who do ...
8
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2answers
948 views

When can I use $\wedge$ instead of curl?

It seems in some circles the wedge product is used in preference to curl. I have a basic understanding of Green and Stokes' formula, I wish to use the $\wedge$ notation from now on. Can someone tell ...
8
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1answer
675 views

Ambiguity with Dirac Notation

When using Dirac notation, how do we distinguish the difference between the inner product and the action of a covector on a vector? As I understand it, $\vert x \rangle$ is an element of say a ...
8
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4answers
3k views

Is there a recognised standard for typesetting quantum mechanical operators?

Firstly, I wasn't sure exactly where to put this. It's a typesetting query but the scope is greater than $\TeX$; however it's specific also to physics and even more specific to this site. I've ...
8
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1answer
2k views

Difference between $\partial$ and $\nabla$ in general relativity

I read a lot in Road to Reality, so I think I might use some general relativity terms where I should only special ones. In our lectures we just had $\partial_\mu$ which would have the plain partial ...
7
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4answers
1k views

How are electric flux calculations not double integrals?

A disk of radius 0.10 m is oriented with its normal unit vector $\hat{n}$ at 30$^{\circ}$ to a uniform electric field $\vec{E}$ of magnitude 2000 N/C. What is the electric flux through the disk? I ...
7
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2answers
3k views

Bra-Ket Notation

I'm having difficulty understanding the bra-ket notation used in quantum mechanics. For instance, take the notation used in the question Is there a relation between quantum theory and Fourier analysis?...
7
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2answers
691 views

Position of Indices in Einstein's Summation Convention

Would there be a difference between the following tensor quantities? $$ {A_\gamma}^\mu {B_\mu}^\rho $$ and $$ {A^\mu}_\gamma {B_\mu}^\rho $$ Would both of these expressions give the same result as ...
7
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2answers
681 views

Why isn't invariant notation common?

In principle, one can write quantities in a manifestly invariant - rather than covariant - fashion in e.g. special relativity. For example, rather than writing just $x^\mu$, we could write the basis ...