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2
votes
2answers
462 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 $|\psi_i>$ ...
1
vote
2answers
195 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 ...
2
votes
2answers
8k 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: What does the y with the line over it represent? And also, does the ...
6
votes
1answer
715 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
431 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
265 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
191 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 ...
3
votes
6answers
1k 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 ...
2
votes
4answers
341 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
69 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
182 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
1answer
2k 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
298 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
221 views

Notation for two variables with same dimensions [duplicate]

What symbol represents "has the dimensions of", as in "x has the dimensions of d"? Does such a symbol exist?
6
votes
2answers
546 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
414 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? $$V=\frac{1}{2}\left(\frac{d^2 V}{{dq_i}{dq_j}}\right)_0$$
7
votes
4answers
878 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
158 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})= ...
6
votes
5answers
925 views

What is the meaning of following expression $C=\frac{\delta Q}{dT}$ mathematically?

Our professor raised the following question during our lecture in Statistical Physics (even so it's related to Thermodynamics): Many text books (even Wikipedia) writes wrong expressions (from ...
1
vote
2answers
652 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). ...
1
vote
1answer
551 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
439 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
67 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
326 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, ...
4
votes
3answers
191 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
323 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
412 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
750 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 $\frac{d^2r}{dt^2}$ ...
3
votes
3answers
344 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
871 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 ...
1
vote
2answers
447 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?
5
votes
1answer
453 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
350 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
125 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 ...
2
votes
1answer
377 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
90 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
272 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 "$a\left|V\right>$" . ...
7
votes
4answers
745 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
403 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 ...
27
votes
1answer
4k 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 ...
15
votes
4answers
3k 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. Transcription: ...
5
votes
2answers
656 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
4k 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
562 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
93 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
268 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 $1s^0$.
22
votes
4answers
4k views

Mathematically-oriented Treatment of General Relativity

Can someone suggest a textbook that treats general relativity from a rigorous mathematical perspective? Ideally, such a book would Prove all theorems used. Use modern "mathematical notation" as ...
0
votes
2answers
312 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
586 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
296 views

Notation of plane waves

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