Questions tagged [notation]
This tag is for questions on the meaning, history, and usage of various symbols and notation that are used to denote different quantities in physics. Don't forget to mention the reference, where you encountered those notations.
1,646
questions
3
votes
1
answer
3k
views
Commutator of Pauli Matrices in two qubit system
For two qubits 1 and 2 with Pauli Matrices $\sigma_{x_1}, \sigma_{x_2}, \sigma_{z_1}, \sigma_{z_2}$, prove that:
$$[\sigma_{x_1} \sigma_{x_2}, \sigma_{z_1} \sigma_{z_2}] = 0$$
I am very confused ...
- 363
0
votes
1
answer
912
views
Derivative with tensor indices
I have trouble figuring out derivatives in tensor notation in SR. I haven't been able to find a simple recipe for writing down a solution. For example what would be the solution to the following ...
- 3
1
vote
2
answers
210
views
What does the $j$ mean in this notation?
This section of Introduction to Quantum Mechanics by Griffiths is talking about the Maxwell Stress Tensor. I don't quite understand what the $j$ means on the left side of the "$=$" sign (for either of ...
- 239
0
votes
1
answer
1k
views
Does an antiproton have a proton number of 1 or -1
I have a disagreement with someone; they have written this equation:
$$
\,^{0}_{0}\gamma\to\,^1_1p+\,^1_1\bar p
$$
I disagree, and say that the anti-proton should have a proton number of -1, not 1. ...
- 888
1
vote
1
answer
1k
views
Decoding the character table
The following is character table of water molecule
I would like to know
(1)What does the last 2 column in the table indicate?
(2) How to deduce the functions in the last column?
- 190
0
votes
0
answers
446
views
Intensity in phasor notation
Following these notes:
http://www.colorado.edu/physics/phys4510/phys4510_fa05/Chapter6.pdf
This is likely just an artifact of me getting confused by notation and not understanding vectors or how to ...
- 163
0
votes
1
answer
775
views
Adjoint ket vectors in Dirac notation?
In books on quantum physics you often see things like $\left(A|\Psi\rangle\right)^\dagger=\langle\Psi|A^\dagger$. However, $|\Psi\rangle:=\Psi\in\mathcal{H}$ is a vector and $\langle\Psi|:=\Psi^\ast\...
- 1,167
2
votes
3
answers
6k
views
How is the isospin quantum number calculated?
$$\Lambda^+_c$$ and $$\Sigma_c^+$$ are both made up of the same quarks, and have the same I_3, but have different isospin quantum numbers. How is the isospin quantum number determined? Also is the ...
- 31
0
votes
2
answers
319
views
Error in Jackson's 'Classical Electrodynamics' definition of Matrix Multiplication (Eq. 6.142)?
I am reading Jackson's 'Classical Electrodynamics' (3rd Edition), and as an exercise I was trying to go through equation 6.142 on page 268. I was wondering if he got this definition of the matrix ...
- 165
0
votes
1
answer
235
views
Dual spaces in Dirac's notation
If I have a certain operator $A$ as well as the following stationary state $|\psi _0\rangle$, and I know that $A|\psi_0\rangle =0$, can I say that $\langle \psi _0|A^\dagger$ also equals zero?
- 464
0
votes
1
answer
125
views
What are CL contours?
I am reading about the precise measurement of top quark mass from: http://arxiv.org/abs/1510.04483
In the second page there is this statement
"The 68% and 95% CL contours for the indirect ...
- 812
0
votes
1
answer
425
views
Straighforward source on GR tensor index notation?
I'm very confused by the notation used in General Relativity. For example, how are indices changed for the Lorentz transformation matrix $\Lambda$ with its components $\Lambda_\mu^{\text{ }\nu}$ or $\...
1
vote
2
answers
119
views
What is this notation using $\psi$ and $J$ to represent particles in a quark-based interaction?
The $c\bar{c}$ meson decays to a lighter meson in the following reactions: $$\psi(3686)\rightarrow J/\psi(3097)+\eta^0$$ $$\psi(3686)\rightarrow J/\psi(3097)+\pi^0.$$
My aim is to find out which ...
- 4,595
1
vote
1
answer
854
views
Finding the components of B in the Electromagnetic field tensor
I have a bit of confusion about how magnetic field components are written in function of the field tensor.
I have the metric $(-,+,+,+)$ so my field tensor is this
$$
F^{\mu \nu} \, = \,\left(\begin{...
- 2,327
0
votes
2
answers
191
views
Very simple index notation question
Trying to understand index notation in the context of spacetime. If I have $x^{\mu}$
and then set $\mu=\phi$
(for example), is it acceptable to then write $x^{\phi}$
or should I just write $\phi$...
- 3,029
3
votes
2
answers
183
views
What does $14.2 \pm 0.1$ mean?
I need to experimentally determine some value $Z = 3X+Y$ where $X$ and $Y$ are measurements. I was given the value for $X$, let's say $X = 14.2\pm 0.1$.
Up to now I thought that if I read something ...
- 195
-1
votes
1
answer
103
views
Meaning of the notation $\partial_{\log x}$
I am reading this paper, and there is the notation $\partial_{\log x}$ in (6.21) on page 17. What does this notation mean?
- 257
8
votes
2
answers
1k
views
Position of Indices in Einstein's Summation Convention
Would there be a difference between the following tensor quantities?
$$ {A_\gamma}^\mu {B_\mu}^\rho $$ and $$ {A^\mu}_\gamma {B_\mu}^\rho $$
Would both of these expressions give the same result as ...
- 81
2
votes
1
answer
1k
views
Sign of the Minkowski metric and proper time
As I understand it the space-time interval $\sigma$ is defined as
$\sigma^2=\eta_{\alpha \beta}x^\alpha x^\beta$. Why is it that some books define the metric with the signs (-,+,+,+) and some with (+,-...
- 992
-3
votes
1
answer
2k
views
Why isn't kilogram written as square kilogram ($\mathrm{kg^2}$) but meter is? [closed]
I was wondering why some notations can be written with square and some can't.
0
votes
3
answers
116
views
Index problem in change of action under spacetime dependent translation
I have two questions, and I'll address them while explaining my calculation and my, probably banal, uncertainties.
We're basically deriving the Energy-Momentum tensor for a scalar field from Noether ...
- 2,327
0
votes
1
answer
61
views
Is the complex conjugate of $|01 \rangle$ equal to $\langle 1 0|$ or $\langle 0 1|$?
I can't seem to deduce this from the basic rules.
On the one hand, I think complex conjugation distributes of tensor products, so I would expect $|01 \rangle^* = (|0 \rangle |1 \rangle)^* = \langle ...
- 753
7
votes
2
answers
7k
views
What is the quantum number $F$ in spectroscopic notation?
In the energy levels of some atoms, like Be, you sometimes see $S(F=0)$, $S(F=1)$ and these are further divided into sublevels $m_F = -1, 0, +1$. I know this $F$ does not stand for the orbital angular ...
- 203
0
votes
1
answer
123
views
What is the correct symbol for writing the deviation between measurements?
I have multiple measurements and I want to indicate that the difference between the lowest deviation and the highest deviation is between a number and another number. For example, when calculating the ...
- 554
2
votes
1
answer
945
views
What does this symbol $\odot$ mean?
While reading through a physics textbook, I came across the use of sub-scripted ☉s.
Here's the context:
Stars between 0.5M☉ and 10M☉ will evolve into red giants...
I'm assuming it's to do with the ...
- 1,819
1
vote
1
answer
153
views
How to use this strange operator with double factorials of the photon number operator?
In a few quantum physics papers I saw an operator proportional to this one:
$$\hat{N}=\frac{(\hat{n}-1)!!}{\hat{n}!!},$$
where $\hat{n}=\hat{a}^{\dagger}\hat{a}$ and $!!$ is the double factorial.
Any ...
- 2,166
0
votes
4
answers
192
views
Should the ° symbol move after the temperature unit to indicate addition/subtraction?
When I was in university, I had a physics lecturer who insisted that when adding or subtracting a certain change in temperature to a known temperature that the unit of the change in temperature be ...
2
votes
2
answers
263
views
Regarding the Dirac Hamiltonian's use of summation notation:
Einstein summation notation, as I understand it:
By writing $A_i B^i$ one implicitly means a sum over elements of the rank 1 tensors A and B. The key is the contraction of an "up" and a "down" index. ...
- 285
2
votes
1
answer
172
views
Difference between $ \left | \psi \right > \left < \psi \right| $ and $ \left < \psi \right | \left . \psi \right> $
On our physics class we were told that $ \left | \psi \right > \left < \psi \right| = \hat{I} $, where $\hat{I}$ is the identity operator. And I cant see the difference between $ \left | \psi \...
- 53
1
vote
3
answers
292
views
Why is $\frac{d^2}{dx^2}=\left(\frac{d}{dx}\right)^2$ justified in the equation for the square of the momentum operator?
The square of the momentum operator $\hat p$ from the time independent Schrödinger equation is $$\hat p^2=-\hbar^2\frac{d^2}{dx^2}\tag{1}$$ in the one dimensional case.
So if we solve this equation ...
- 2,460
10
votes
3
answers
12k
views
Raising and Lowering Indices of Levi-Civita Symbols (+---) metric?
There are a few questions here regarding upper and lower indices of the levi-civita symbol but I haven't been able to find an answer to my exact question. I am working on a problem where I start out ...
- 13.9k
0
votes
1
answer
117
views
What is this notation in the context to the radial wave equation: $R(r)=\frac{u(r]}{r}$?
Here is the whole problem, I understand the context... but I never encountered this notation before. It looks like set notation but it is not defining a set of real numbers.
Problem: Writing the ...
- 712
0
votes
1
answer
58
views
Order used when listing units
When writing out measurements, what order should be used when listing the units? e.g., Why is newton-metre (N m) used instead of metre-newton (m N)?
I encourage you to include resources/links/etc.
- 145
0
votes
1
answer
72
views
Can I say that two different quantities are zero? [duplicate]
I started to learn basics of physics in a university. I know that it is wrong to compare for example pressure and length, like $2\mbox{ Pa}\ne 2\mbox{ m}$. But from algebra I know that $0=0\cdot 2\...
13
votes
2
answers
7k
views
Bra-Ket Notation
I'm having difficulty understanding the bra-ket notation used in quantum mechanics. For instance, take the notation used in the question Is there a relation between quantum theory and Fourier analysis?...
- 133
0
votes
2
answers
759
views
Transforming matrix element for Coulomb interaction from position to momentum space
I'm stuck with the Dirac notation in this calculation. I have the Coulomb interaction given by the matrix $$\langle x|V|x' \rangle = V(|x-x'|) = \frac{1}{|x-x'|}$$
and I want to go to the momentum ...
- 2,805
1
vote
1
answer
541
views
In which argument is the scalar product linear, and in which is it antilinear?
I've been reading about Hilbert spaces and I noticed something that bugs me. All the math books state that the scalar product is linear in its first argument and antilinear in the second, while all ...
- 78
2
votes
0
answers
834
views
Notation for vectors and covectors
This is probably a very simple question, and I think I know the answer, but I cannot find a place to solidly confirm this.
So if I want to write a vector $\mathbf{V}$ in terms of its contravariant (...
- 981
0
votes
1
answer
173
views
What is this notation with an un-sandwiched comma in the subscript?
I have a scalar deflection potential (in the study of weak lensing) and in the book (Schneider, Kochanek and Wambsganss's Gravitational Lensing: Strong, Weak and Micro) I have the following passage:
...
- 4,595
6
votes
1
answer
872
views
Equations of motion for action with differential forms/Hodge star
I'm trying to compute the equations of motion for an action, but I'm not really familiar with the notation and so I'm not entirely sure what to do. It's a non-linear sigma model, describing maps $X: \...
- 751
1
vote
2
answers
116
views
Question about Physicists' Convention
Many times I hear physicists say "$x$ is finite" when what they really mean is $x>0$ or $x\neq0$.
Why is that?
Zero is a valid finite number. What's wrong with simply saying $x$ is strictly ...
- 2,004
72
votes
10
answers
10k
views
Should zero be followed by units? [duplicate]
Today at a teachers' seminar, one of the teachers asked for fun whether zero should be followed by units (e.g. 0 metres/second or 0 metre or 0 moles). This question became a hot topic, and some ...
- 1,819
0
votes
1
answer
377
views
Confusion with basic bra-ket properties
Given a particle whose position can be anywhere on the $x$-axis we may write the following:
$$\hat x|x'\rangle=x'|x'\rangle$$
and so we may write the expansion postulate as:
$$|\psi\rangle=\int\...
- 69
3
votes
2
answers
176
views
Question about completely antisymmetric unit pseudotensor
In a book, it says for transforming a completely antisymmetric unit pseudotensor from non-curvilinear system $x'$ to curvilinear system $x$, one can use
$$E^{iklm}=\frac{\partial x^i}{\partial x^{'p}...
- 880
0
votes
1
answer
134
views
Questions about metric tensor
Why $$g_{ik}g^{kl}=\delta ^l_i~?$$ That is why the two quantities on LHS are reciprocal tensor to each other? Is this a definition? Or it can be proved in general?
- 880
7
votes
4
answers
15k
views
Is Del (or Nabla) an operator or a vector?
Is Del (or Nabla, $\nabla$) an operator or a vector ?
\begin{equation*}
\nabla\equiv\frac{\partial}{\partial x}\vec{i}+\frac{\partial}{\partial y}\vec{j}+\frac{\partial}{\partial z}\vec{k}
\end{...
- 129
1
vote
2
answers
268
views
State Ket Interpretations
I have a question that came from lecture earlier in the semester, that I never fully understood:
Let's suppose that we have an electron, that at $t=0$ is in an eigenstate of $\hat{S}\bullet\hat{n}$, ...
- 344
0
votes
0
answers
102
views
Does $Z^2$ always mean $ZZ^*$ in quantum mechanics?
So I was listening to video on quantum mechanics and the following happened:
$$ |c\rangle = a|x\rangle + b|y\rangle$$
This was for polarized light, where $a$ and $b$ were probability amplitudes. The ...
- 443
3
votes
1
answer
591
views
Is Dirac's notation really necessary?
One thing that's always bothered me in Dirac's notation is that it assumes that the Hilbert space contains a "continuum basis" of vectors $|x\rangle$, which happen to be eigenvectors of an operator $X$...
- 83
1
vote
2
answers
173
views
Tensor index question
I am looking at the solution in the book "Problem book in Relativity and Gravitation" for problem 10.6. I don't think I need to go into the details of the problem (I will do so if need be) because I ...
- 981