The notation tag has no wiki summary.
0
votes
1answer
42 views
Some Dirac notation unclarities
Q1:
Ok so i have come to a point where i know that $\Psi(r,t)$ which we denote only by $\Psi$ can be represented in a Hilbert space by a vector which we denote $\left|\Psi\right\rangle$. Does this ...
4
votes
2answers
77 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 ...
1
vote
2answers
47 views
Vector $\vec{z}$ and its conjugate transpose $\overline{\vec{v}^\top}$ - is it the same as $\left|z\right\rangle$ and $\left\langle z \right|$
Lets say we have a complex vector $\vec{z} \!=\!(1\!+\!2i~~2\!+\!3i~~3\!+\!4i)^T$. Its scalar product $\vec{z}^T\!\! \cdot \vec{z}$ with itself will be a complex number, but if we conjugate the ...
2
votes
1answer
49 views
Scalar top quark (stop) pair production
A rather simple question:
Starting from an electrically neutral state, pairs of top quarks are produced as top and anti-top, and denoted as $t\bar t$.
Now the production of pairs of scalar top ...
3
votes
2answers
108 views
Difference between slanted indices on a tensor
In my class, there is no distinction made between,
$$
C_{ab}{}^{b}
$$
and
$$
C^{b}{}_{ab}.
$$
All I know, and read about so far, is the distinction of covariant and contravariant, form/vector, etc. ...
17
votes
8answers
1k 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" ...
2
votes
2answers
142 views
Inner Product Spaces
I am trying to reconcile the definition of Inner Product Spaces that I encountered in Mathematics with the one I recently came across in Physics. In particular, if $(,)$ denotes an inner product in ...
-1
votes
1answer
102 views
Vector Addition — Direction
Say we have three forces $F_1, F_2, F_3$, such that
$$
F_1 + F_2 - F_3 = 0\hspace 10mm (1)
$$
And let us say that $F_1$ and $F_2$ have the same direction and magnitude, and that $F_3$ has double the ...
0
votes
0answers
54 views
Curvilinear abscissa confusion
How's exactly defined the curvilinear abscissa in kinematics? Surfing on the net I found different definitions:
a) Fixed a point $O$ and a direction, the curvilinear abscissa $s$ at a point $P$ is ...
2
votes
1answer
99 views
What does the notation $c = [1:\beta]$ mean?
I have been reading a online-book/blog/material on Quantum Mechanics, when I encountered a notation on a page and I have no idea what it means. See if you can help.
Here's the link and follows the ...
4
votes
0answers
92 views
Is it correct to sum over either index of the metric the same way?
I don't know if the following is correct, i want to compute the following derivative
$$\frac{\partial }{\partial (\partial_{\mu}A_{\nu})}\left(\partial^{\alpha}A^{\beta}\partial_{\alpha}A_{\beta} ...
1
vote
0answers
44 views
Reaction coordinate as a function of atomic positions
I'm going over some (molecular dynamics) related literature - specifically the derivation of the Weighted Histogram Analysis Method (WHAM).
As a quick backdrop WHAM is a method for stitching ...
-2
votes
1answer
146 views
Differences between orthogonality and Kronecker delta function? [closed]
If $i$ and $j$ are two variables then Kronecker delta is written as
$$\delta_{i,j}~:=~\begin{cases}1 \hspace{3mm} \mbox{if} \hspace{3mm} i=j,\\
0 \hspace{3mm}\mbox{if} \hspace{3mm}i \neq ...
1
vote
1answer
267 views
Wave function and Dirac bra-ket notation
Would anyone be able to explain the difference, technically, between wave function notation for quantum systems e.g. $\psi=\psi(x)$ and Dirac bra-ket vector notation?
How do you get from one to the ...
2
votes
2answers
85 views
Double Pendulum
The equations of motions for the double pendulum is given by
$$\dot{\theta_1} = \frac{6}{ml^2}\frac{2p_{\theta1} - 3\cos(\theta_1 - \theta_2)p_{\theta2}}{16 - 9\cos^2(\theta_1 - \theta_2)}$$
and ...
0
votes
2answers
70 views
Proper notation for normalized scalar?
I have not been able to find a resource to tell me the standard notation for a normalized scalar value. Normalized vectors (i.e. unit vectors) are typically denoted by placing a hat over the ...
2
votes
2answers
151 views
In Dirac notation, what do the subscripts represent? (Solution for particle in a box in mind)
So the set of solutions for the particle in a box is given by
$$\psi_n(x) = \sqrt{\frac{2}{L}}\sin(\frac{n\pi x}{L}).$$
In Dirac notation $<\psi_i|\psi_j>=\delta_{ij}$ assuming $|\psi_i>$ ...
0
votes
2answers
77 views
When do I apply Significant figures in physics calculations?
I'm a little confused as to when to use significant figures for my physics class. For example, I'm asked to find the average speed of a race car that travels around a circular track with a radius of ...
0
votes
2answers
105 views
From differentials to differential equations
Suppose I have a function of time $t$ and position $(x,y)$ such that
\begin{equation} p_t \,dt = p \,dy - p_x (1-x) \,dx + p_y \,dy\end{equation}
where the subscript denotes a differentiation. In this ...
1
vote
1answer
449 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:
http://postimage.org/image/oe7hb9cy3/
What does the y with the line ...
2
votes
1answer
176 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 ...
4
votes
1answer
162 views
Clarifications about Poisson brackets and Levi-Civita symbol
I need some clarifications about Poisson brackets.
I know canonical brackets and the properties of Poisson Brackets and I also know something about Levi-Civita symbol (definition and basic ...
0
votes
2answers
62 views
Meaning of juxtaposition of vectors
I came across some notation that I can't quite understand:
$$ \hat{r}\hat{r} - \textbf{1}_3$$
where $\textbf{1}_3$ is the 3$\times$3 identity matrix, $\hat{r}$ is a unit 1$\times$3 vector, and the ...
1
vote
2answers
125 views
Notation for differential operators and wave function math
I know that $[\frac {d^2}{dx^2}]\psi$ is $\frac {d^2\psi}{dx^2}$ but what about this one $[\frac {d^2\psi}{dx^2}]\psi^*$? Is it this like $\frac {d^2\psi\psi^*}{dx^2}$ or this like $\frac ...
1
vote
6answers
407 views
Is H=H* sloppy notation or really just incorrect, for Hermitian operators?
I saw it in this pdf, where they state that
$P=P^\dagger$ and thus $P$ is hermitian.
I find this notation confusing, because an operator A is Hermitian if
$\langle \Psi | A \Psi \rangle=\langle A ...
1
vote
4answers
170 views
Is there a default notation for 4-vectors while handwriting?
In printed paper 3-vectors can be denoted bold italic while 4-vectors can be denote just bold.
While handwriting 3-vectors are denoted by arrows above letters.
Is there a similar way to denote ...
2
votes
1answer
58 views
Uncertainty writing
This will sound like a silly question, but I don't recall that my professors ever though me what this means. For example:
X=1.2345(6) units
This is uncertainty, that much I do know, but does it ...
2
votes
2answers
97 views
SI units with more than one prefix in fractions
Is it (in the view of SI) correct to note units with more then one prefix? I discuss this since several months with friends, but we could not find a proper source for our statements yet.
Examples for ...
0
votes
0answers
99 views
Circuit symbol for ammeter with output [closed]
What is the correct symbol for an ammeter that measures 0..200 mA and generates 0..2 V proportional output?
0
votes
1answer
239 views
Mutual Inductance and the Dot Convention
Can anyone please explain me, the dot convention in coil systems (Mutual and self inductance) with some related images to understand..?
3
votes
2answers
192 views
What are $\partial_t$ and $\partial^\mu$?
I'm reading the Wikipedia page for the Dirac equation:
$\rho=\phi^*\phi\,$
......
$J = -\frac{i\hbar}{2m}(\phi^*\nabla\phi - \phi\nabla\phi^*)$
with the conservation of probability ...
0
votes
1answer
78 views
Notation for two variables with same dimensions
What symbol represents "has the dimensions of", as in "x has the dimensions of d"? Does such a symbol exist?
6
votes
2answers
298 views
What the circled integral?
What the circled integral
$$
\oint
$$
means?
I saw this symbol in a lot of books about advanced physics.
How is his definition? What kind of integral it is? It is used only in physics or also in ...
2
votes
2answers
251 views
Meaning of subscript in $V=\frac{1}{2}\left(\frac{d^2 V}{{dq_i}{dq_j}}\right)_0$
This is probably a simple question, but what does the subscript $0$ mean in the following expression?
$$V=\frac{1}{2}\left(\frac{d^2 V}{{dq_i}{dq_j}}\right)_0$$
5
votes
4answers
270 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.
...
0
votes
0answers
80 views
Quantum Mutual Information scaling
Wikipedia provides a simple definition of Quantum Mutual Information:
$$I(\rho^{ab})= S(\rho^{a}) + S(\rho^{b}) - S(\rho^{ab})$$
where in terms of relative information we have:
$$I(\rho^{ab})= ...
1
vote
2answers
139 views
Is the letter delta generally only used to express change in variable or quantity?
I was speaking with a friend of mine earlier and he said "Oh look, delta, the sign of uncertainty" (he doesn't study physics often so had only seen in in Heisenberg's Uncertainty Principle equations). ...
2
votes
1answer
157 views
Symbol for dashpot/damper (in a harmonic oscillator)
In diagrams that contain the dashpot symbol, sometimes the mass is attached to the "interior" end of the dashpot, other times the mass is attached to the "base" end.
For example, consider the ...
2
votes
1answer
180 views
Meaning of $d\Omega$ in basic scattering theory?
In basic scattering theory, $d\Omega$ is supposed to be an element of solid angle in the direction $\Omega$. Therefore, I assume that $\Omega$ is an angle, but what is this angle measured with respect ...
1
vote
1answer
59 views
What is $k_B$ in the context of this question?
Answering the following question
1000 atoms are in equilibrium at temperature T. Each atom has two
energy states, $E_1$ and $E_2$, where $E_2 > E_1$ . On average, there are 200
atoms in the ...
4
votes
2answers
176 views
Standard notation reference
I'm searching for a compresensive and somewhat complete list of suggested standard notation (the symbols one ought to use in (theoretical) physics and also mathematics).
Is there such a collection, ...
0
votes
1answer
75 views
In what subfields and how fare can the “naive limit” of special relativity be carried?
Even if many interesting similarities between the classical and the quantum mechanical framework have been worked out, e.g. in the subject of deformation quantization, in general, there are some ...
0
votes
1answer
128 views
Spectroscopic notation $s$, $p$, $d$, $f$, $\ldots$
$s$ is sharp, $p$ for principal, $d$ for diffuse, $f$ for fundamental.
Where do all those term come from? I do not see any link with the corresponding shapes.
0
votes
3answers
162 views
Why is 'the period' marked as letter T?
I'm not a native English speaker and I was wondering, why 'the period' got the letter $T$.
I've asked myself the question when I was thinking about stuff related to the frequency. I.e.:
$f$ - ...
0
votes
1answer
252 views
Relationship between acceleration, velocity and position
I'm learning some applications for equation of motion. But I'm failing to relate velocity, acceleration and position.
If $v=\frac{dr}{dt}$ and $a=\frac{dv}{dt}$, why $a$ is $\frac{d^2r}{dt^2}$ ...
2
votes
3answers
235 views
How to distinguish 4D and 3D vectors in handwriting?
Usually vectors are denoted with bold font in printbooks and with arrows above in handwriting.
In Thorn's e al. Gravitation, 4D vectors are denoted with bold and 3D vectors with bold italic. How to ...
0
votes
3answers
251 views
Differential squared vs. differential of squared
Why it is said that
$$\frac{dx^2}{dt^2}=\upsilon^2$$
I can only understand the following one:
$$\left (\frac{dx}{dt} \right)^2=\upsilon^2$$
Edit:
Excerpt from Landau's Mechanics:
Execrpt from ...
0
votes
2answers
133 views
When to use $f$ and when $\nu$ signifying frequency?
When to use $f$ and when $\nu$ signifying frequency? I guess that when you mean frequency of electromagnetic wave, you use $\nu$, and $f$ otherwise?
4
votes
1answer
273 views
Why is $L^2$ norm of the gradient called kinetic energy?
I'm reading Lieb-Loss's book 'Analysis', chapter 7. The authors refer to the following integral:
$$\tag{1} \lVert \nabla f\rVert_2^2=\int_{\Omega}\lvert \nabla f(x)\rvert^2\, d^nx $$
as the kinetic ...
1
vote
2answers
242 views
Question with Einstein notation
Let’s consider this equation for a scalar quantity $f$ as a function of a 3D vector $a$ as:
$$ f(\vec a) = S_{ijkk} a_i a_j $$
where $S$ is a tensor of rank 4. Now, I’m not sure what to make of the ...
