Questions tagged [notation]

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2
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1answer
99 views

How is the complex integration done for the Wigner function in coherent state representation?

$$W(\alpha)=\frac{1}{\pi^2}\int e^{\lambda\alpha^*-\lambda^*\alpha} \operatorname{Tr}\left[ \hat{\rho}e^{\lambda\hat{a}^\dagger} e^{-\lambda^* \hat{a}} \right] e^{-\frac{|\lambda|^2}{2}} \, d^2\lambda....
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2answers
366 views

Representing tensor products using Dirac's bra-ket notation

I know, that $$ \uparrow \equiv \left[ \begin{array} { l } { 1 } \\ { 0 } \end{array} \right] $$ and $$ \bigg| \frac { X - i Y } { \sqrt { 2 } } \bigg \rangle = \sqrt { \frac { 3 } { 8 \pi } } \frac { ...
1
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1answer
74 views

How to differentiate Capacitance (Italized C) and Coloumbs (regular C) on paper [closed]

I am doing a question on capacitance and coulombs. I got the answer correct, but I was wondering how a physicist, when doing the calculation on paper, would differentiate a C and C?
1
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1answer
113 views

Peskin and Schroeder: derivation of Dirac fields commutator

I'm perplexed by the following non numbered equation at page 54 of Peskin & Schroeder, right between $(3.92)$ and $(3.93)$ $$ [\psi_a(x),\overline{\psi}_b(x)]=\int\frac{d^3p}{(2\pi)^3}\frac{1}{...
0
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1answer
81 views

Definition of angular velocity vector of $B$ in $A$ - Strange notation

I found the following definition of angular velocity vector of B in A at page 49 of the book "Thomas R. Kane, Peter W. Likins, David A. Levinson - Spacecraft Dynamics - McGraw-Hill (1981)": The ...
3
votes
1answer
47 views

What does $\delta$ represents in FLUCTUATION-DISSIPATION THEOREM?

i am trying to follow the following tutorial. I keep seeing $\delta$ over functions such as $\delta F(x)=F(x)-\langle F(x)\rangle_t$ (Eq 14.4) in this and in other tutorials and questions here. What ...
0
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1answer
50 views

What do I get by multiplying a 0 operator on a 0 eigenvector?

I don't know how to write the equation form. Assuming my notation as Dirac notation, what do I get from $$ ( 0 | 0 | 0 ) ~?$$
1
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2answers
114 views

Notation in Heisenberg Uncertainty Relation: greater than with tilde: $\gtrsim$

In "The Road to Reality" (pg. 523), Roger Penrose writes: Heisenberg's uncertainty relation tells us that the product of these spreads cannot be smaller than the order of Planck's constant, and ...
1
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2answers
127 views

Proving the raising and lowering of the raising and lowering operator

I am given a written proof of $\hat A^{\dagger}[u_n] = \sqrt{n+1} \ u_{n+1}$, and from it, and told to similarly prove $\hat A[u_n] = \sqrt{n} \ u_{n-1}$. However, in the written proof for $\hat A^{\...
0
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1answer
60 views

Electrodynamics : Problem with Notations for fields $\vec{(\vec{r},t)}$ and $\vec{B}(\vec{r},t)$(complex and real notations)

I'm sutyding a course on electrodynamics and am stuck on a few lines I can't make sense of. The professor uses $$\vec{E}(\vec{r},t) = \vec{U_0} cos (\vec{k}\cdot \vec{r} - \omega t + \phi)$$ (so far, ...
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1answer
1k views

What is a homogeneous magnetic field?

What does it mean when one says that a magnetic field is a homogeneous magnetic field?
2
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2answers
61 views

What does a double parenthesis in a quoted value ─ like e.g. 157(3)(3) ─ mean?

Sometimes, in journal articles, the author writes a number followed by two parenthesis. For example, $157(3)(3)$, where it seems that the first parenthesis shows uncertainty in the last digit (here, $...
0
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1answer
98 views

Why is $\partial_{\mu}x^{\nu} = \delta^{\nu}_{\mu}$?

In Blundell's book on QFT, one can find the following Is this because of: $$\partial_{\mu}x^{\nu} = \partial_{\mu}x^{\nu^{'}} \partial_{\nu^{'}}x^{\mu}$$ $$\partial_{\mu}x^{\nu} = \Lambda_{\mu}^{\...
0
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1answer
191 views

The hermitian conjugate of anti-linear operator

Some quantum mechanics books tell us that the definitions of hermitian are If $\langle\psi|A\phi\rangle=\langle B\psi|\phi\rangle$ for linear operators, then $B=A^\dagger$ If $\langle\psi|C\...
1
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1answer
459 views

Shorthand error notation (with brackets) accros decimal point

I have a small doubt regarding the use of shorthand error notation, i.e. $6.626070150(81)$ instead of $6.626070150 \pm 0.000000081$. When the error has 2 s.f. (such as when the error is just over $1 \...
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2answers
63 views

Moment of Inertia equation for small volume

Below is the equation of the moment of inertia for small volume elements, $\Delta m$ $$I = \lim_{\Delta m_i \to 0} \sum_{i} r^2_i \Delta m_i = \int r^2 dm$$ Can someone please explain it to me on ...
0
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2answers
146 views

Identities from ket to bra vector

I have three questions. Lets say I have a state $\lvert\psi\rangle = \hat{c}_1^\dagger \lvert 0 \rangle $. Is the corresponding bra then given by $\langle\psi\lvert= \hat{c}_1 \langle 0\lvert $ ? ...
1
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2answers
325 views

Inner product in QFT

When we write inner product in QM for example $\langle\psi\rvert x \psi\rangle$it means (in position space) $\int\psi^*(x,t)x\psi(x,t)dx$. But when we write, in QFT, $\langle0\rvert0\rangle=1$ what ...
0
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1answer
47 views

Using diagonality in Einstein notation

Given a diagonal matrix $D$, with diagonal elements given by vector $\mathbf{d}$. Representing this in Einstein notation gives $$ D_{ij} = \delta_{ijk} d_k $$ where $$ \delta_{ijk} = \begin{cases}...
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2answers
58 views

Strange super script notation $^{(4)}R$ in the textbook Numerical Relativity

In Numerical Relativity by Thomas W. Baumgarte and Stuart L. Shapiro. There are bunch of superscript $(4)$ over $T,\Gamma, R$ i.e. $^{(4)}\Gamma^a_{bc}$ _ $^{(4)}R_{abcd}$ _ $^{(4)}R$ ... (...
0
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1answer
226 views

Proof of invariance of scalar product under rotations, using index notation

So I have got the following question: Show that the scalar product of two cartesian vectors $p_i\cdot q_i$ is invariant under coordinate transformations (orthogonal transformations) Now I know ...
1
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1answer
106 views

Quick question on choosing a gauge (E.g. Lorenz gauge)

I have been quite confused when I read about choosing a gauge. For example we have the gauge transformation $$ A_\mu\longrightarrow A_{\mu\prime}= A_\mu+\partial_\mu\alpha, $$ and we can choose any $...
3
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1answer
74 views

Dot convention inductors in series: what is going on

So I'm really confused with mutual inductors and dot convention. If your answer is going to be a link to any website I can assure I read them all and that only left me more confused. So here are my ...
0
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1answer
99 views

Path Integral Notation [closed]

In my Statistical Field Theory lectures, I was told that $$Z=\int \mathcal{D}\phi\ e^{-F[\phi]}=\int\prod_{k<\Lambda}d\phi_k\ e^{-F[\phi_k]}$$ I want to clarify that I understand the ...
0
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1answer
44 views

Operator $A$ only act on the neighboured state or operator but not the entire expression?

In state vector formalism $A|\psi(x)><u(x)|=(A|\psi(x)>)<u(x)|$, where $A$ only act on $|\psi(x)>$ However, in terms of wave formalism, suppose $A$ is the well known $\frac{d}{dx}$. ...
1
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2answers
134 views

Covariant and contravariant coordinates - index notation

I am learning about electrodynamics and have recently been introduced to the four vector. I also come fresh to the idea of covariant four vectors and contravariant four vectors. My question concerns ...
3
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1answer
56 views

A Question about Index Notation of a Scalar Product [closed]

Could anyone please explain why an index $k$ is added to the scalar product of the velocities (squaring the velocity) in the figure below? Can't we use the same index $j$ for the second factor? $$\...
0
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1answer
305 views

Is $\nabla=\nabla'$? Nabla operator acting on $r^n$

I have been taught that $$\nabla r^n =\text{gradient of }r^n =n r^{n-1}\ \hat{\boldsymbol r}$$ but in introduction to electrodynamics by Griffith (4th edition) on page 173, $\nabla' r^n$ is given by $-...
6
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1answer
247 views

Why is Penrose's diagrammatic notation for tensor operations not widely used? [closed]

Strictly speaking this is a mathematics question rather than a physics question, but since it is about a way of dealing with tensor bundles that is very remote from what is done in math, and very ...
1
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0answers
100 views

Most used convention about Christoffel symbols

Just a simple question: what is the most used form for Christoffel symbols, (1) or (2), see below: (1) $$\Gamma_{ij}^{k} = g^{kl}\Gamma_{lij}$$ and then, we have: $$\Gamma_{lij}=\Gamma_{lji}$$ (2) $...
4
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0answers
86 views

When was the phrase “beta function” of renormalization first used?

My question is a historical one: when was the phrase "beta function", as it pertains to the renormalization-group equations, used in physics? I am talking about this beta function: $$\beta_g\equiv \...
2
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1answer
98 views

Weinberg's Lectures on Quantum Mechanics - Definition of Momentum Operator

In Weinberg's "Lecture on Quantum Mechanics" (2nd edition, page 79) in equation 3.5.11, about the momentum operator acting on states definite position, the minus sign is missing. Is this just a typo ...
-3
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4answers
164 views

What is the difference between $\vert-\rangle$ and $\vert+\rangle$?

I understand that a Qubit can be represented in the form of $$\vert\psi\rangle=\alpha \vert0\rangle+\beta\vert1\rangle$$ where $\alpha$ and $\beta$ are complex numbers and the $\alpha^2$ and $\beta^2$ ...
0
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3answers
101 views

Why is $\langle c \cdot f|g\rangle=c^*\langle f|g\rangle$?

Why is $\langle c \cdot f|g\rangle=c^*\langle f|g\rangle$? $c$ is a complex number and $c^*$ is the conjugate. I think that $\langle c \cdot f|g\rangle=c\langle f|g\rangle$ because that's how scalar ...
1
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0answers
82 views

What are the different versions of the Schrodinger Wave Equation? [closed]

Whilst I have been looking at Quantum Mechanics online, I have come across lots of different versions of the SE. What is the difference between them, why are there some with Dirac Notation and others ...
0
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2answers
80 views

Explanation of notation change between 1D and 3D T.I.S.E.?

I am currently reviewing this webpage, near the end it shows how the one-dimensional time independent Schrondinger equation can easily be extended to three dimensions. My question is specifically ...
1
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1answer
371 views

How can $2\pi/\omega = T$, when it is equal to $\lambda/v$?

I can conceptually understand that $2π/$angular frequency will result in the period. $2π$ represents a full cycle, and $\omega$ represents the angle per second of the wave. Then, it follows that a ...
-1
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1answer
82 views

Notation in One-dimensional Schrodinger equation [closed]

I am reading a book where it write the one-dimensional stationary Schrodinger equation as $$ [-\frac{\hbar^2}{2m}\frac{d^2}{dζ^2}-Γ{\rm sech}^2(bζ)]ψ(ζ)=Eψ(ζ). $$ It is known that the equation is ...
1
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1answer
96 views

Abuse of Calculus [duplicate]

I'm following Professor R. Shankar's Fundamentals of Physics course on YouTube. There I saw him doing manipulations of Calculus I never saw before. Here it goes, $$\newcommand\deriv[2]{\frac{\mathrm ...
7
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6answers
332 views

In quantum mechanics, is $|\psi\rangle$ equal to $\psi(x)$?

So I'm going through my notes and I think I've confused myself. We often imply $$ |\psi\rangle \to \psi(x)\\ \langle\psi| \to \psi(x)^* $$ for instance when we talk about eigenvalue equations we ...
4
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1answer
162 views

A question about the notation of the Standard model

The ${\rm SU(2)_L}$ doublets, for example, the left-handed quark doublets $Q_{iL}\equiv(u_{iL}, d_{iL})^T$ are assigned quantum numbers $(\textbf{3},\textbf{2})_{+1/6}$, which means $Q_{iL}$ are ...
0
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1answer
73 views

Notation issue for mixed tensors

When I am asked to evaluate, $\mathbf{U^{\alpha}_{~,~~\beta}}$ for all $\alpha$ and $\beta$, what does it mean? I have not able to understand this notation. In case of $\mathbf{g(~~,~\bar{A})}$ I ...
0
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2answers
392 views

Antisymmetric part of a tensor with Levi-Civita symbol

How to write the antisymmetric part of a tensor in general? It has been asked here but I want to write it using the Levi Civita symbol. I have thought of: $$A^{\mu_1} A^{\mu_2} - A^{\mu_2} A^{\mu_1}...
1
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1answer
208 views

Tensor Product Explanation

I'm currently doing a research project involving 3 particle spins and have developed a simple function for the Hamiltonian: I understand how to code my work but the physics behind it is unfamiliar ...
2
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3answers
116 views

Quantum Mechanics Notation

I'm studying the Bloch Sphere and just wanted to ask what this notation means: $|\psi\rangle = \alpha|1\rangle$ for example I'm just not familiar with the notation in this context if anyone could ...
-1
votes
2answers
65 views

Expression of central force

Is $$\vec{F}(\vec{r})=F(r) \hat{r}$$ actually a formula or a general notation for central force? what is conveyed through this expression? I'm in the beginning stage of learning this concept so please ...
1
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3answers
105 views

What does this equation regarding Kepler's laws of planetary motion actually mean?

I'm doing a project in multivariable analysis regarding Kepler's laws of planetary motions and the following equation was a recommended equality to use, but none of the variables were actually defined:...
1
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1answer
52 views

What to do with an extra index in the definition of a tensor?

I came across this definition of a tensor while reading some vector calculus literature This definition contains the index $\ell$ in the last term, however the tensor itself only depends on $j$ and $...
1
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0answers
37 views

Non-differential total exact element notation question [duplicate]

I have questions regarding the notation in thermodynamics books of "d bar" (instead of delta) for the non-differential total exact elements like for work $\delta W$. When did it appear? Where are ...
0
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2answers
109 views

Operator in Dirac notation

Lets say I have a operator $\textbf{A}$ = $ \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} $ in a canonical basis {|a⟩ ,|b⟩}. The operator can be re-written in Dirac notation as $\textbf{A}$=...

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