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1answer
16 views

Notation of polarization of light

Upon my research of polarization of light I stumbled upon the following formula: What do the three dots mean? I have never seen them before. Edit: Found this notation in the book "Nonlinear fiber ...
0
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1answer
12 views

Meaning of these terms for stress fields?

I'm from a math & comp sci background and I'm currently looking at facture theory which deals with stress fields. Can someone explain to me what the following terms represent in the context of a ...
0
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1answer
45 views

Where does this relativistic relation involving the delta function come from?

\begin{equation} \int\delta(E^2-\mathbf{p}^2-m^2)dE=\frac{1}{2E_\mathbf{p}} \end{equation} Shouldn't integrating the delta function like this just give 1?
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3answers
127 views

Technical question about 2-forms

A technical question about the electromagnetic tensor, but before that, it is know if, say, instead of being $$F_{\mu\nu}=\partial_{\mu}A_{\nu} - \partial_{\nu}A_{\mu}$$it were ...
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0answers
48 views

What's the advantage of using bra-ket notation over inner-product notation? [migrated]

Both notations look pretty similar, and appear similar when undergo algebraic operations. Apart from personal taste (aesthetics) concerning commas (<,>) vs. pipes (<|>), what is (are) the ...
0
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1answer
37 views

Voltage and volume, same SI symbol, how to discern between the two? [closed]

Both are SI quantities that use the same symbol, namely $V$. It annoys me that I might be working with the wrong unit even though it's easy to see if it's voltage or volume by looking to the whole ...
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0answers
46 views

Contraction of Kronecker delta = 4 [duplicate]

This suggests, as a shortcut notation, the concept of lowering indices; from any vector we can construct a (0, 1) tensor defined by contraction with the metric: $$A_\nu ≡ g_{\mu\nu}A^\mu$$ so that ...
2
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2answers
163 views

Relativity question about 4-velocity

Given a 4-velocity $u^0$, how do you find $u_0$? Do you use $u_{\alpha}u^{\alpha} = -1$?
3
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3answers
193 views

Notation of vectors

It's very common to see $\text{F} = 30 \text{ N}$ when the problem is unidimensional. Yet, force is a vector. Shouldn't I write $|\overrightarrow{F}| = 30 \text{ N}$? Because if I write ...
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0answers
55 views

What is the meaning of symbols $\delta f$ and $\delta^2f$?

Professor was using these symbols to derive the continuity equation. He defined the infinitesimal mass as $\delta^2m=\rho \delta V$ and the mass that leaves some closed boundary $\partial V$ as ...
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0answers
8 views

Ambiguity with circuit symbols [migrated]

If I wanted to draw say a verical thermistor in a circuit diagram, it can look like any one of these four: Is there a convention for which one to pick, or are all of them valid in any situation ...
3
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3answers
44 views

What is nuclide notation referring to? Only the nucleus or the whole atom?

sorry that this is an easy question but I am just a bit confused about nuclide notation. When you say e.g. $^{240}_{94}\text{Pu}$, are you referring to the atom of $\text{Pu}$ or only its nucleus? It ...
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3answers
94 views

What's the correct link between Dirac notation and wave mechanics integrals?

In wave mechanics when we compute the expectation value of energy we write the following $$\left<\hat{H}\right>=\int_{-\infty}^\infty\mathrm{d}x\ ...
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2answers
113 views

Using mega (=10^6) when writing by hand? [closed]

I just solved a problem which had answer 1.7*10^6 m (m=meters) If I wanted to write this using M=10^6 it would be 1.7 Mm, which if I write it by hand would look like "1.7 mm" which is confusing. Is ...
2
votes
1answer
39 views

Notation of angular momentum operators vs numbers

I'm reading about finding the mass of quarks in mesons. In the lecture notes, it says We need to find $\langle\boldsymbol{s}_q\cdot\boldsymbol{s}_\bar{q}\rangle$. Since $L=0$, then ...
1
vote
1answer
45 views

Electric current notation

Depending on the source, I sometimes read $\frac{\delta q}{dt}$ , $\frac{dq}{dt}$ or even $\frac{\delta q}{\delta t}$ (rare) Wich one is the correct notation ? In theory we are to know if a ...
2
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2answers
43 views

What does a left-right arrow in a tensor formula mean?

I need help with some some notation I've not seen before. Is using the left-right arrow in this formula $$[P^μ,M^{ρσ}]=i\hbar(g^{\mu\sigma}P^\rho-(\rho\leftrightarrow\sigma))$$ equivalent to writing ...
1
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1answer
117 views

Questions about the formalism of Quantum Mechanics

I have to do a presentation on this. I'm not expected to do something really detailed, but I'm not understanding the mathematical formalism. I would like to receive general answers to these questions: ...
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2answers
54 views

Understanding notation regarding particles states and wavefunctions

In the development in my notes of second quantisation I have a problem in understanding notation. We start by considering a basis $\psi_i(\mathbf{r})$ for the Hilbert space of single particle ...
0
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1answer
72 views

Spinor notation in general relativity

I have a somewhat broad/big question, and I know that there are many references for it available out there. However, so far I couldn't find anything that I can really understand, that's why here is my ...
2
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0answers
27 views

Atomic physics, determining levels and terms

In atomic physics I understand there a configurations, terms and levels. I think levels for instance appear because of spin-orbit interactions, so that terms are split. But I'm confused about the ...
1
vote
1answer
79 views

Quantum Mechanics Notation

Generally we have that $$|\psi\rangle=\int_{all space} \psi(\mathbf x)|\mathbf x\rangle d^3\mathbf x$$ and therefore $\psi(\mathbf x)=\langle\mathbf x|\psi\rangle$. When discussing the mutual ...
1
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1answer
43 views

Two-component formalism and four-component formalism [closed]

When deriving the Dirac equation for spin-1/2 particles, we realize that the wave function must be four-component. In some works, people use two-component wave function for calculation. So, my ...
2
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0answers
43 views

Index notation for a Lagrangian with second derivatives

I'm finding the field equations for a hypothetical Lagrangian with dependence on the second derivative of a scalar field, $L\left(\phi,\phi_{,\mu},\phi_{,\mu\nu}\right)$, and in the analogue to the ...
-1
votes
1answer
39 views

What does $\bar{x}_{\textrm{el}}$ represent?

In the context of centroids and moments, what do $\bar{x}_{\textrm{el}}$ and $\bar{y}_{\textrm{el}}$ represent? For example: $$\bar{x}L = \int \bar{x}_{\textrm{el}}dL$$ Some references that use ...
0
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1answer
57 views

What does 400kW(e) mean?

I am trying to read a document and it says a power grid is 400kW(e) what does this mean?
0
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1answer
43 views

Apply Hamiltonian to position eigenstates

Let $\hat{H}$ be the free Hamilton operator, is it then true that $$\langle {\bf r}| \hat{H} ~=~ - \frac{\hbar^2}{2m} \Delta \langle {\bf r}|~?$$ Where $\Delta\equiv \nabla^2$. I currently don't see ...
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0answers
38 views

Notation - d.o.f.'s for Grassmann delta functions in a SUSY field theory amplitude

I was reading the following paper http://arxiv.org/pdf/1306.2962v1.pdf as I stumbled upon an issue concerning counting and assigning the Grassmann degrees of freedom that appear in grassmann delta ...
1
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2answers
56 views

How do I represent $A$ transpose $A$ in indicial notation?

I know this question sounds lame, but the book I am following doesn't use the answer I expect and it has been using a similar notations everywhere else which has confused me. I think Q[Any tensor] ...
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3answers
124 views

Justifying the notation $\langle x\ |\ \psi\rangle$ [duplicate]

I came across this expression: $$\langle x\ |\ \psi\rangle=\psi(x)$$ How can it be justified? I understand the LHS as an inner product, and the RHS just as a function of the parameter $x$.
0
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2answers
47 views

Interaction Hamiltonian in the interaction picutre

The Schrodinger and Heisenberg pictures make sense to me. But the interaction picture which is a hybrid of the two does not. Author of this text first splits the Hamiltonian up as ...
0
votes
1answer
36 views

Meaning the symbol, $W$ and $dW$

What's the difference between $W$ and $dW$? They are both work done and have similar formulae (same dimension). But I don't know the difference between them. $dW$ here ISN'T power.
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3answers
89 views

Suppose $\phi(x)$ is a field, how should I interpret $\partial^\mu\phi$ and $\partial_\mu\phi$?

I am really confused by the sub and upperscript notation sometimes. It might be really trivial but I have a difficult time interpreting the following things in for example this Lagrangian ...
1
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3answers
115 views

Tensor product in quantum mechanics

In Cohen-Tannoudji's Quantum Mechanics book the tensor product of two two Hilbert spaces $(\mathcal H = \mathcal H_1 \otimes \mathcal H_2)$ was introduced in (2.312) by saying that to every pair of ...
1
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1answer
47 views

Permutation operator and second quantization

I just read that a permutation operator $P_{i,j}$ acts on a product state $|a_1,...,a_n \rangle \in H^n$ by $$P_{i,j} |a_1,...,a_i,a_j,...a_n\rangle = |a_1,...,a_j,a_i,...a_n \rangle .$$ Now my ...
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2answers
81 views

What are $\mu$ and $\nu$ in $g_{\mu\nu}$ metric?

What are $\mu$ and $\nu$ in $g_{\mu\nu}$ metric? Consider the metric $g_{\mu\nu} = \begin{pmatrix} 1 & 0 &0 \\ 0 & r^2 & 0\\ 0 & 0 & r^2\sin^2\theta \end{pmatrix}$
1
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1answer
49 views

What does a colon mean in hydrodynamics equations?

In some hydrodynamics book I saw a notation like $e:e$ where $e$ is a matrix (shear stress tensor). This double dot product is in a scalar equation, so the result of this operation must be scalar. I ...
0
votes
1answer
63 views

Indexed Gradient operator on trigonometric functions

$$\nabla_{i}\nabla_{j}\Big(\frac{\sin(kR)}{R}\Big)$$ Where $R$ is the distance between particle $i,j$. And $k$ is a constant I took $\nabla_{i}=\frac{\partial}{\partial R_{i}}$ and ...
1
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1answer
99 views

Tensor product notation in quantum mechanics

I'm a bit confused about the use of Tensor products in Quantum mechanics. For instance if two electrons are in the state $\frac{1}{\sqrt{2}}(a(r_1)b(r_2)-b(r_1)a(r_2))\otimes \lvert \downarrow ...
4
votes
1answer
65 views

Computation of $T^{\mu\nu}$ from Lagrangian density $\mathscr{L} $

I am trying to understand how upper and lower indices are connected when computing the energy-momentum tensor. In particular, I found the simple problem where the Lagrangian density is given as ...
10
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4answers
551 views

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: ...
0
votes
1answer
44 views

Energy-Momentum Tensor with mixed indices

I know that $T_{\mu\nu}$ is the Energy-Momentum Tensor and $T=g^{\mu\nu}T_{\mu\nu}$, but does anyone know what $T^{\nu}_{\mu}$ is and how its calculated?
1
vote
1answer
49 views

Is there a correct yet more compact way to write these equations?

I've got the following equation which denotes the total absorbance $A$ as determined by the sum of the absorbances of individual molecules: \begin{equation} A(\nu,c_{1},...,c_{n}) = \sum_{mol=1}^{n} ...
8
votes
3answers
1k views

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

How would you denote symbolically, "Equilibrium happens given that ..."?
0
votes
0answers
39 views

Is it ever appropriate to write $| \phi(t)>$

I am trying to solve the Schrodinger's wave equation $\hat H |\psi(x,t)> = E|\psi(x,t)>$ using separation variables so that $\psi(x,t) = \psi(x)\phi(t)$ Solving the equation involves the step ...
14
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1answer
2k views

Meaning of an image on Feynman's shirt

Is there any physical meaning of the image on Feynman's T-shirt?
0
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1answer
90 views

Electric flux of a closed surface, $\Psi = Q $ or $\Phi =\int\vec{E}\cdot d\vec{A}$

I have problem with the equation of electric flux. I use one book of fundamental physics and another book of electromagnetic engineering; the two of them give different equations for electric flux. ...
0
votes
1answer
68 views

What does this Hodge dual symbol $\star_3$ mean?

We know that in this $$\star {f(...)}$$ the $\star$ represents the Hodge dual. But in this: $\star_3 f(...)$ what does specifically the $\star_3$ symbol mean?
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5answers
152 views

Is $ds^2$ just a number or is it actually a quantity squared?

I originally thought $ds^2$ was the square of some number we call the spacetime interval. I thought this because Taylor and Wheeler treat it like the square of a quantity in their book Spacetime ...
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6answers
200 views

Is $∣1 \rangle$ an abuse of notation?

In introductory quantum mechanics it is always said that $∣ \rangle$ is nothing but a notation. For example, we can denote the state $\vec \psi$ as $∣\psi \rangle$. In other words, the little arrow ...