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11
votes
2answers
370 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 ...
6
votes
5answers
785 views

What is the meaning of following expression $C=\frac{\delta Q}{dT}$ mathematically?

Our professor raised the following question during our lecture in Statistical Physics (even so it's related to Thermodynamics): Many text books (even Wikipedia) writes wrong expressions (from ...
3
votes
1answer
81 views

Confusion about the Kronecker delta symbol

I am not sure I understand what the short-hand anti-symmetrization means. I.e. I know that $$\delta_{cd}^{[ab]} ~=~ \frac{1}{2}(\delta_{c}^{a}\delta_{d}^{b} - \delta_{c}^{b}\delta_{d}^{a})$$ but how ...
1
vote
2answers
123 views

Understanding basic quantum mechanics notation

I was talking with a guy about energy levels of an atom in a magnetic field. He said that energy levels are shifted and that, if you want know how much, you have to analyze this: for 1s state: ...
3
votes
4answers
220 views

What is the right order of creation operators?

I started to learn some basics of second quantisation and specifically its use in quantum chemistry. Currently I'm reading this book by Péter R. Surján, and here is small excerpt from it. If one ...
0
votes
1answer
54 views

How are dimensions indicated in physics equations?

The universe is often described as being 4-dimensional (having 3 spatial dimensions + the dimension of time). Some theories (such as some string theories) consider the universe as having even more ...
0
votes
0answers
49 views

Coordinate Symbol confusion in general relativity

In a previous post (Finding the metric tensor from the Einstein field equation?), the equation used lambda, rho mu and nu (not sure of the names of the letters!) for the Ricci tensor and swapped to a, ...
7
votes
1answer
220 views

Why is the Lane-Emden equation written the way it is as opposed to some other typical form?

The Lane-Emden equation is typically written as $$\frac{1}{\xi^2} \frac{d}{d\xi} \left( \xi^2 \frac{d\theta}{d\xi} \right) = -\theta^n,$$ which makes sense given the derivation on the Wikipedia page. ...
1
vote
1answer
50 views

How is $\langle \psi |\psi \rangle$ meaningful in Dirac notation?

I'm reading Quantum Mechanics - A Modern Development, and it explains bra-ket notation, if I understand it correctly, as follows. Let $V$ be a vector space, and let $F$ be a linear function mapping ...
1
vote
1answer
25 views

Strange definition of a two-level system by the Bloch vector

A two-level system can be described by a density operator involving the Bloch vector $$ \vec{r}; \quad r_x = Tr(\rho X); \quad r_y = Tr(\rho Y); \quad r_z = Tr(\rho Z) $$ as $$ \rho = \frac{I + ...
0
votes
0answers
32 views

Needed small explanation of the notation in this paper [duplicate]

There is this paper: http://digital.csic.es/bitstream/10261/43192/1/p6374_1.pdf In equation (36) of this, the second line ($\omega^{+ij} =\dots$), there is a term ...
2
votes
1answer
92 views

Dirac Notation Question Appearing In a Projection

So I have a part of the energy eigenvalue equation that look like this: $$ \delta(\hat{x})|n\rangle $$ Where n is the energy basis of the Hamiltonian I'm considering. To deal with this, I tried ...
1
vote
2answers
71 views

Tricks at manipulating creation/annihilation operators

Manipulation of terms in algebras different from the standard one (e.g. boolean algebra) can be a bit unnatural but there are always shortcuts that can help you. I was wondering if there is a list ...
1
vote
2answers
45 views

Symbol in energy formula vs amplitude

Can someone tell me what does the symbol mean in the formula for energy compared to amplitude? Looks like a partial infinity sign, almost like a fish symbol.
0
votes
0answers
11 views

Need Quick reference card for scientific notation and symbols for paper reading

Hi can any one lead me to resource for symbols and notation and their meaning used for writing/publishing/scientific writing paper eg: Δ or δ means difference . ∀ means 'for all' x | y pipe mean ...
1
vote
0answers
17 views

Vibrational quantum notation

Reading articles on spectroscopy I often see this notation: 30001 <- 01101, 00011 <- 00001 in context of molecular ...
2
votes
2answers
143 views

What's the symbol for the antiparticle of the delta plus baryon?

It can't be $\Delta^-$ since that is another particle also made up of quarks (not antiquarks). I can think of four possibilities: $\overline\Delta^+$ $\overline{\Delta^+}$ $\overline\Delta^-$ ...
2
votes
3answers
117 views

Index notation with Navier-Stokes equations

This is an index-notation question rather then the NS one: For incompressible flow and Newtonian fluid, the continuity equation is denoted with: $$\frac{\partial u_i}{\partial x_i} = 0, $$ which ...
2
votes
2answers
92 views

Physical interpretation of order of tensor indices

Using positional index notation with tensors is common. For example, the following simple equation from Carroll's Spacetime and Geometry text (eq. 3.146): $$ R = R^\mu_{\,\,\mu} = ...
3
votes
1answer
122 views

Correct tetrad index notation

There seems to be some different conventions on the indexes of the tetrad. I am wondering which is the standard, which is correct, and which is an abuse of notation. In Sean Carroll's notes and in ...
10
votes
5answers
1k 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 ...
0
votes
1answer
42 views

Really quick question about the order of operations in the Lorentz force

I'm trying to calculate the Lorentz force for a particle in a uniform electric Field, E and magnetic field B. The formulas is $$F=q(E+v\times B)$$ I'm just wondering what the order of operations is ...
2
votes
1answer
135 views

Reaction coordinate as a function of atomic positions

I'm going over some (molecular dynamics) related literature - specifically the derivation of the Weighted Histogram Analysis Method (WHAM). As a quick backdrop WHAM is a method for stitching ...
22
votes
4answers
3k 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 ...
2
votes
3answers
88 views

What does the $c$ in $eV/c^2$ stand for?

I have been wondering(also searching) for what does the $c$ in eV/$c^2$ stand for? (For example, mass of the electron is $0.511 \, \text{MeV}/c^2$.) I have read that this unit has been derived from ...
0
votes
1answer
79 views

Why is $d$ generally not used instead of $r$ in Newton's derivation of force of gravitation? [closed]

In Newton's law of gravitation we take distance between two bodies $r$ and represent it in the form of $r^2$? Why don't we take distance as $d$?
2
votes
1answer
81 views

Why does Dirac write $\langle\xi'|\overline{f(\xi)} = \overline f(\xi ')\langle\xi'|$?

Starting on page 41 of Dirac's The Principles of Quantum Mechanics, he defines $f(\xi)$ in general to be that linear operator which satisfies $$f(\xi)|\xi'\rangle = f(\xi')|\xi'\rangle\tag {34}$$ ...
0
votes
0answers
45 views

How to read this state in quantum physics?

I am having a little trouble understanding this state: $$ \,^3D\left[3/2\right]_{1/2} $$ What does the $[3/2]$ indicate here?
2
votes
2answers
6k views

What does y with a line over it represent?

I've been asked to complete this chart and have never come across this symbol before, nor can I find anything about it on google: What does the y with the line over it represent? And also, does the ...
0
votes
2answers
126 views

A tensor summation question

With the definition of the tensor: \begin{equation} J_{ij} = I_{ij} - \tfrac{1}{3}\delta_{ij}I^{k}_{k}, \qquad i,j,k\in\{1,2,3\}, \end{equation} I have seen the quantity: \begin{equation} ...
1
vote
2answers
50 views

Standard Usage of the word “per”

Math guy here. What is the usual meaning of "x per y per z?" Is this (ignoring details) (x/y)/z or x/(y/z)? Sorry to be mundane.
5
votes
3answers
276 views

Tensor product notation convention?

For two particle state, the Dirac ket is writren as $$\lvert\textbf{r}_1\rangle \otimes \lvert\textbf{r}_2 \rangle. $$ Then how do we write its bra vector, $$\langle\textbf{r}_1\rvert \otimes ...
1
vote
1answer
51 views

What does the first column in the “decay modes” table mean (in Particle Data Group documents)?

As a follow-up to this more general question, what are the values in the first column of each of the "decay tables" in a PDG document describing? What are those things in the first column? Are they ...
1
vote
1answer
82 views

Riemann curvature tensor notation in Wald

This question is entirely on tensorial notation in Wald's General Relativity. When specifying the properties of the Riemann tensor on pg39, he states: $R_{[abc]}^{\quad \ \ \ d} = 0$ and For the ...
0
votes
1answer
67 views

Notation in the book Symmetry by Hermann Weyl

I'm having troubles understanding a notation of the symmetry groups in a book "Symmetry" by Hermann Weyl. On the page 80 of the 1952 Princeton University Press edition of the book, Weyl lists the ...
1
vote
2answers
93 views

$\exp(i\alpha\hat {\bf n}\cdot{\bf \sigma} )=\cos\alpha I+i(\hat {\bf n}\cdot{\bf \sigma})\sin\alpha$

Could anyone tell me $\hat {\bf n}\cdot{\bf \sigma}$ is defined in such way? In the book they have not defined what is $n_z,n_x,n_y$. It is from Quantum Computing: From Linear Algebra to Physical ...
3
votes
1answer
118 views

What does the notation $\Psi_k/(\Psi_k,\Psi_k)^{1/2} $ mean?

I am currently reading the paper "Gravitation and quantum mechanics for macroscopic objects" by F. Karolyhazy (1966). In his paper, he uses certain notation that I haven't come across before (he also ...
5
votes
2answers
216 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 ...
3
votes
0answers
125 views

Convention in physics for [],{} and operators (QM)

I got a little mixed up with the convention in physics. Usually a hat means an operator. For a given electron-ion Hamiltonian $\hat{H}_{e-n}$, what are the difference between these: 1) ...
0
votes
2answers
90 views

Using bra-ket notation?

Am I using Bra-ket notation correctly? I want to define a superposition of the states, $|0\rangle$ and $|1\rangle$. Is it simply? $|0\rangle + |1\rangle$ I can't find any non-technical information ...
3
votes
0answers
78 views

The states of the adjoint representation correspond to the generators

I understand the definition of the adjoint representation. It uses structure constants as matrix components of generators, but I can't understand meaning of the states $|X_{a}\rangle$. What does ...
0
votes
2answers
96 views

Is there a difference in handwritten nabla $\vec{\nabla}$ with an overset arrow and typeset nabla $\nabla$?

According to some physicist at KIT it is usual to write the following when using pen and paper: whereas in typeset texts you write $\nabla$. Is that true? Are there sources for this convention?
5
votes
2answers
200 views

Unknown letter ℑ used in an equation

I need to write by hand the equation from the attached snapshot but I really don't know what letter is that seen in the front of square brackets [ . Can anyone help ...
0
votes
4answers
111 views

Dot product of vector and its derivative with respect to time? How does $L \cdot\frac{dL}{dt} = \frac{1}{2}\frac{d(L^2)}{dt}$? [closed]

How does: $$L \cdot\frac{dL}{dt} = \frac{1}{2}\frac{d(L^2)}{dt}$$ where L is a vector (I dunno how to make it bold in the equation). How do they reach to this right hand side equation? And what is ...
8
votes
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 ...
0
votes
3answers
67 views

Understanding ket notation and the unitary matrix, what does a/the unitary matrix represent?

I am reading over this paper http://www.scottaaronson.com/thesis.pdf, specifically page 24 under "Quantum computing cheat sheet". The author is explaining ket notation and how it relates to ...
5
votes
2answers
205 views

A confusion about notation in Goldstein

On treating systems of particles, Goldstein starts with the consideration that whenever there are $k$ particles on a system, the $i$-th one obeys the relation $$\dfrac{d}{dt}{\bf p}_i = {\bf ...
2
votes
1answer
40 views

What is the meaning of $\%E$ on a graph?

I'm reading the book The New Science of Strong Materials by J.E. Gordon. He writes when we plotted (...) breaking strain, against thickness, we found it did not matter what the whiskers were made ...
-1
votes
1answer
116 views

Why can't we do some basic algebra in tensor calculus?

I have a very, very stupid question on the basics of tensor calculus. Consider $R_{ij} = 0$. 1)If I expand the ricci tensor $R_{ij}= g^{lm}R_{iljm}=0$. Now, my question is that, why can't we divide ...
1
vote
1answer
36 views

How you call the constant $\alpha$ within the heat equation in general and in terms of electromagnetism?

The heat equation or diffusion equation does contain a constant $\alpha$. $$\frac{\partial u}{\partial t} - \alpha \nabla^2 u=0$$ How is it called? I'm interested in a general name which can be ...