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4
votes
3answers
169 views

In what subfields and how far can the naive limit $c\rightarrow\infty$ 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
205 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
232 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
406 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
288 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
477 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
230 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
341 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
284 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 ...
6
votes
1answer
98 views

$\pm$ (light-cone?) notation in supersymmetry

I would like to know what is exactly meant when one writes $\theta^{\pm}, \bar{\theta}^\pm, Q_{\pm},\bar{Q}_{\pm},D_{\pm},\bar{D}_{\pm}$. {..I typically encounter this notation in literature on ...
1
vote
1answer
261 views

Rocket drive and conservation of momentum

I am currently reading through some lecture notes of Physics 1 and in a chapter about the dynamics of the mass point, there is an example covering the rocket drive. Let $v$ be the velocity of the ...
2
votes
2answers
75 views

Another question about Shankar's notation

I have another question on the notation in Shankar. I think it's sloppy, but I also may just be misunderstanding it. Again, this is at the very beginning of the math intro. He has: $$a\left| V ...
1
vote
2answers
238 views

Question on notation in Shankar's Quantum Mechanics - math intro on vector spaces

I'm just beginning Shankar's 2nd edition Quantum Mechanics and having some trouble with notation. He defines his vectors as "$\left|V\right>$" . And with a scalar multiplier as "$a\left|V\right>$" . ...
5
votes
4answers
290 views

Is there a recognised standard for typesetting quantum mechanical operators?

Firstly, I wasn't sure exactly where to put this. It's a typesetting query but the scope is greater than $\TeX$; however it's specific also to physics and even more specific to this site. I've ...
1
vote
2answers
250 views

Why no basis vector in Newtonian gravitational vector field?

In my textbook, the gravitational field is given by$$\mathbf{g}\left(\mathbf{r}\right)=-G\frac{M}{\left|\mathbf{r}\right|^{2}}e_{r}$$ which is a vector field. On the same page, it is also given as a ...
20
votes
1answer
2k views

Differentiating Propagator, Greens function, Correlation function, etc

For the following quantities respectively, could someone write down the common definitions, their meaning, the field of study in which one would typically find these under their actual name, and most ...
13
votes
4answers
2k views

What does Peter Parkers formula represent?

Okay, so the trailer for the new Spider Man movie is out and appearently our friendly physicist from the neightborhood came up with something. However I can't find out what this is. ...
4
votes
2answers
497 views

Bra-ket notation and linear operators

Let $H$ be a hilbert space and let $\hat{A}$ be a linear operator on $H$. My textbook states that $|\hat{A} \psi\rangle = \hat{A} |\psi\rangle$. My understanding of bra-kets is that $|\psi\rangle$ is ...
3
votes
1answer
2k views

What does $\Psi^*$ mean in Schrodinger's formulation of Quantum Mechanics?

I am not a physics student. In one of my courses, some fundamental concepts of Quantum mechanics were needed, so I was going through them when I stumbled upon this. It says $$\text{probability} = ...
2
votes
2answers
385 views

Correct application of Laplacian Operator

Not a physicist, and I'm having trouble understanding how to apply the Laplacian-like operator described in this paper and the original. We let: $$ \hat{f}(x) = f(x) + \frac{\int H(x,y)\psi(y) ...
5
votes
3answers
81 views

which letter to use for a CFT?

In math, one says "let $G$ be a group", "let $A$ be an algebra", ... For groups, the typical letters are $G$, $H$, $K$, ... For algebras, the typical letters are $A$, $B$, ... I want to say ...
1
vote
2answers
229 views

Subshell notation for hydrogen cation?

Looking at $s$,$p$,$d$ configuration for atoms & ions: Since a hydrogen cation $H^+$ has no electron, how would the subshell notation be written? My best estimate would be $1s^0$.
0
votes
2answers
245 views

How is an arbitrary operator usually denoted in quantum mechanics?

Which symbols are usually used to denote an arbitrary operator in quantum mechanics, such as O in the following example? $O \mbox{ is Hermitian} \Leftrightarrow \Im{\left< O \right>} = 0$
1
vote
1answer
369 views

state vector notation

I've never taken a quantum mechanics class, but I find myself now using principles developed in the quantum theory of angular momentum. One particularly confusing aspect that I'm struggling with is ...
1
vote
2answers
265 views

Notation of plane waves

Consider a monochromatic plane wave (I am using bold to represent vectors) $$ \mathbf{E}(\mathbf{r},t) = \mathbf{E}_0(\mathbf{r})e^{i(\mathbf{k} \cdot \mathbf{r} - \omega t)}, $$ $$ ...