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0
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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
votes
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
votes
1answer
97 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
76 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?
6
votes
5answers
157 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 ...
2
votes
6answers
207 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 ...
4
votes
4answers
718 views

Does bra-ket always assume all space?

One thing I never understood about the bracket notation is the limits of the inner product. Given $ \langle \psi∣\psi \rangle$, what can I say about the limits of integration of the inner product? ...
1
vote
2answers
118 views

Bra-ket of products

I was trying to solve the following problem. (Lifted from Modern Quantum Chemistry: Introduction to Advanced Electronic Structure Theory by Szabo and Ostlund) I came across across a solution for ...
2
votes
1answer
297 views

QCD color factors from quark gluon vertices

The color factors in QCD tell us the relative strength of the coupling of a quark emitting a gluon, a gluon emitting a quark-antiquark pair or a gluon emitting two gluons. To calculate let them we ...
9
votes
1answer
121 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 $s$ ...
0
votes
0answers
20 views

Proper nuclear reaction notation for arbitrary species

I am wondering the common way to write a nuclear reaction for an arbitrary species. For instance, for neutron capture on a species $X$: $$^{A}_ZX + n \rightarrow ^{A+1}_{\ \ \ \ \ Z}X'.$$ Is this ...
0
votes
2answers
125 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 ...
-1
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2answers
187 views

What's the symbol behind Einstein's head? [closed]

What's the symbol called that's behind and to the right of Einstein's head in this picture? Bonus if you can tell me what the whole formula is!
0
votes
1answer
117 views

Einstein notation in Electrodynamics

I have a question about the notation used in Electrodynamics, for the Eq.6.5.10. Can anyone tell me why is the sign of the covariant derivative swapped when it's transformed to a contravariant ...
3
votes
2answers
171 views

Why are the quantum numbers $n$ and $\ell$ denoted with those letters?

We have 4 quantum numbers: principal, azimuthal, magnetic and spin (denoted $n$, $\ell$, $m$ and $s$ respectively). I assume $m$ and $s$ are simply the initials of 'magnetic' and 'spin'. Is there any ...
21
votes
2answers
826 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 ...
4
votes
1answer
98 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 ...
0
votes
1answer
70 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 ...
4
votes
4answers
269 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 ...
7
votes
1answer
235 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
81 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
65 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 ...
1
vote
2answers
126 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
21 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
27 views

Vibrational quantum notation

Reading articles on spectroscopy I often see this notation: 30001 <- 01101, 00011 <- 00001 in context of molecular ...
2
votes
2answers
131 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
2answers
239 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 ...
2
votes
3answers
358 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 ...
0
votes
1answer
48 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 ...
0
votes
1answer
88 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
3answers
103 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 ...
1
vote
2answers
237 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: ...
2
votes
1answer
88 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
46 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
173 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: $\overline\Delta^+$ $\overline{\Delta^+}$ $\overline\Delta^-$ ...
1
vote
2answers
61 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
317 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 ...
2
votes
1answer
97 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
1answer
75 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
118 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 ...
1
vote
2answers
112 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
136 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
298 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
139 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
133 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
103 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
156 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?
0
votes
4answers
160 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 ...
5
votes
2answers
218 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 ...