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.
1,791 questions
0
votes
4
answers
180
views
Weird integral notation for work
As part of a thermodynamics class my professors had a weird intergral. Let $\vec F$ be a force acting on a piston. $\vec F = -p A \vec{e_x}$. Since work is $W_{12}= - \int^2_1 \vec F \cdot \vec {dx}$.
...
- 165
0
votes
2
answers
105
views
'Principles of Quantum Mechanics- 4th Edition' - Dirac / Request for help with 'simple' formula
As an amateur who read and enjoyed the integral 'Feynman Lectures on Physics', I am now reading Dirac's 'Principles'.
In §17 - The representation of linear operators - I struggled with a rather '...
0
votes
0
answers
73
views
Why a partial derivative in equation (1.247) of Sakurai's "Modern Quantum Mechanics" 3rd Edition? ($p$ as generator of $\Delta x$ in $x$-basis) [duplicate]
Equation (1.247) is the first one in section "1.7.2 Momentum Operator in the Position Basis" and looks like this (where in his notation a prime after a letter means it's not an operator)
$$
\...
- 101
2
votes
0
answers
145
views
Express stress tensor with Dirac notation and operators
For a system in equilibrium, we know that the stress tensor is expressed as:
$$\sigma_{\alpha\beta}=-\frac{1}{\Omega}\frac{\partial E}{\partial \epsilon_{\alpha\beta}}$$
where $\Omega$ is the volume, $...
- 318
-1
votes
0
answers
144
views
Correct Interpretation of Equations with Indices [migrated]
This is a doubt that arose while studying the tensor product representation of lie algebra. The normalization condition for the generators in any given representation is written as :
$$\langle T_{a}|...
- 529
2
votes
1
answer
274
views
Struggling with doing calculus with Dirac notation
I'm currently studying non-degenerate perturbation theory, and inside my course notes, there was the problem:
"Using the fact that $\hat a|0_0⟩ = 0$, where $a$ is the lowering operator for the ...
- 47
-1
votes
1
answer
91
views
Why are vectors written out in a basis of covectors in general relativity? [duplicate]
I am following a course on general relativity and we are now talking about vectors and covectors. Covectors have lower indices and vectors have upper indices. In my book, they say that any vector $V$ ...
6
votes
4
answers
1k
views
Being rigorous about the chain rule?
Prelim: $s(t)$ is the displacement in 1D, $v(t)$ is the velocity, and $a(t)$ is the acceleration. This question was motivated by the fact that when one tries to actually use chain rule instead of ...
- 245
5
votes
1
answer
136
views
How does index notation work in complex vector spaces with non-degenerate Hermitian forms?
My experience with index notation is strictly in the context of special relativity where the real vector space $V$ is equipped with a symmetric, non-degenerate bilinear form $g:V\times V\to \mathbb{R}$...
- 1,835
3
votes
2
answers
221
views
Why doesn’t $(\Lambda^{-1})^{\mu}_{\,\,\nu}=\Lambda_{\nu}^{\,\,\mu}$ imply $\Lambda^{-1}=\Lambda^T$ for Lorentz boosts?
According to books and lecture notes,
$$\Lambda^{-1}=\eta^{-1}\Lambda^T\eta=\eta\Lambda^T\eta$$
which I have no problem with. Then they write this in index notation as
$$(\Lambda^{-1})^{\mu}_{\,\,\nu}=...
- 127
1
vote
0
answers
47
views
Index order in Einstein notation [duplicate]
I am learning about four-vectors in special relativity in my electrodynamics lecture.
We have learned that under Lorentz transformations $\Lambda$, vectors transform like
$$
x'^{\mu} = \Lambda_{~~~\nu}...
- 11
1
vote
0
answers
78
views
Confusion in $\delta$ and $d$ in the first law of thermodynamics [duplicate]
Some people write First law of thermodynamics of Black Holes as
$$\delta M=\frac{\kappa}{8 \pi} \delta A+\Omega \delta J$$
while others write
$$d M=\frac{\kappa}{8 \pi} d A+\Omega d J$$
$\delta$ and $...
- 1,008
2
votes
0
answers
67
views
Tensor network notation
I am trying to understand the tensor network language for the kicked Ising model. The details of the same are in supplemental material III. I could understand almost all of them with ease. However, I ...
- 183
-1
votes
1
answer
120
views
Question about Schrödinger equation with scalar and vector potentials from Sakurai
This is from page 127 of Sakurai QM:
How did they obtain this result? I understand the factor comes from the Hamilton on the LHS, but how were they able to pull out the factor out of the bra-ket like ...
0
votes
1
answer
142
views
Scientific notation with/vs. complete integers
I got into a fight on the zsh forum over the fact that zsh uses '5.' to indicate the integer 5 but stored as a floating point number. I protested that '5.0' would be better since the trailing dot is ...
- 161