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.

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1answer
78 views

What does this bra-ket equation mean?

I was reading Griffiths Introduction to Quantum Mechanics and I came across this equation: $$\langle \psi_a |z|\psi_b\rangle$$ Where z is direction. I don't understand why there are those subscripts a ...
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$\int dx\, dy\, dz\, d p_x\, dp_y\, dp_z$ Does it have any physical meaning? [closed]

I was reading a Physics book. Then I saw an equation which was looking like this: $$\int dx\, dy\, dz\, d p_x\, dp_y\, dp_z.$$ I was thinking it from just a Calculus book. I can see lots of variable (...
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1answer
58 views

What do some of the symbols in the Schrodinger Equation mean? [closed]

The Time Dependent Schrodinger Equation has the form $$i\hbar\frac{\partial}{\partial{t}}\Psi=-\frac{\hbar^2}{2m}\left(\nabla^2+V\right)\Psi$$ and the Time Independent Schrodinger Equation has the ...
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0answers
33 views

Kroenecker delta/Levi-Civita interaction [closed]

For part d, would the 2 from the kronecker delta change the j in the Epsilon to become E123?
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0answers
28 views

What was actually wrong with vitreous and resinous nomenclature?

What was actually wrong with vitreous and resinous nomenclature? Why was it replaced by nomenclature of positive and negative?
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1answer
57 views

Confusion about the notation for the tangent vector to the FRLW's metric congruence

I want to solve the following problem (Problem 2.2 on Poisson's book "A Relativist's Toolkit"): The FLRW metric is $$\text{d} s^2 = -\text{d} t^2 + a(t)^2 \Bigg(\frac{\text{d} r^2}{1 - kr^2} ...
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1answer
87 views

Equations and functions in physics and mathematics

In physics we can define velocity as the derivative of position. We can write: $$u = \frac{d}{dt}x(t)$$ or $$u = g(t)$$ where $g$ denotes the function after differentation of the position with respect ...
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3answers
926 views

How it is possible that a ket precedes a bra in a matrix expression?

Is it possible to rewrite $\langle a| M|b\rangle$ as $|b\rangle \langle a|M$?
3
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1answer
101 views

Scientific Notation for Different Units of Charge

Sorry in advance for the basic question, I’m pretty new to physics. I’m doing some electromagnetism homework and so far in class we’ve used only nano and micro coulombs in our force and electric field ...
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1answer
91 views

What does the $O$ mean in "$O(v^4)$"?

I am currently studying General Relativity and I am using the book by Schutz. I encountered a problem when I was reading about the gravitational redshift experiment. Here is the website (it is not the ...
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1answer
80 views

Problem in understanding notation of scattering amplitude

The Schrodinger equation: $$ i \frac{d}{d t}\left|\psi_{t}\right\rangle=H\left|\psi_{t}\right\rangle $$ and solutions are given by $$\left|\psi_{t}\right\rangle=U(t)|\psi_\text{in}\rangle \equiv e^{-...
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6answers
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Using differentials in physics [duplicate]

I was lately wondering about the use of differentials in physics. I mean, usually $dx$ is thought of as a small increment in $x$, but does this have any rigorous meaning mathematically. Doubts started ...
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2answers
51 views

Confusion about the summation convention [closed]

In Liouville's system, the kinetic energy has the following form, $$T = \frac{1}{2}\sum_{i}f_{i}(q_{i})\dot{q}_{i}^{2}$$ As one can see, that index $i$ has appeared three times and repeated indices ...
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4answers
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What do $\nabla$ and $\frac{d }{d t}$ mean when they are by themselves?

In QM and QFT, I have seen some equations where they have just the derivative and/or the gradient without specifying what it is acting on. Taken from wiki. This does not make sense to me since I ...
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1answer
68 views

Understanding covariant and contravarient components of vector in Ket notation

I learned about covariant and contravariant vectors in the context of Vector and Tensor analysis and Now I'm learning about it in the context of Linear vector spaces in Dirac ket notation. I'm having ...
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4answers
78 views

Frictional force is proportional to the velocity

I came across the following in Goldstein Book: The frictional force is proportional to the velocity of the particle. Thus its $x$ component has the form $F_{fx}=-k_x v_x$ . Wikipedia says, ...
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2answers
420 views

Issue in deriving Ehrenfest's theorem

Working in Schrodinger picture, while deriving Ehrenfest's theorem, we go - $$ \frac{d}{d t}\langle A\rangle=\frac{d}{d t}\langle\psi|\hat{A}| \psi\rangle $$ $A$ is an operator. Expanding RHS- $$ \...
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1answer
86 views

Confused with 4-vector notation and 4-derivative

I have a lot of trouble finding out what the rules are for doing algebra and calculus with 4-vectors. This example shall illustrate one of my problems: The Lagrangian for a real scalar field is $$\...
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1answer
37 views

Double symmetrization in Einstein index notation

What does the following supposed to give? This appears in equation (3.12) in the following link: https://arxiv.org/abs/1312.5344 (last term) $$A^{(I(J}B^{K)L)} = $$ $$1) \quad \frac{1}{2}(A^{(IJ}B^{KL)...
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1answer
389 views

Index Notation Question

We're busy doing a GR course, and index notation has always been something that confuses me. In particular, is there a difference between the following, and if so, what is it? $A^\mu_\nu$; $A^\mu{}_\...
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1answer
62 views

Why Column Vector is used to Represent Qubit [closed]

While going through the basics of (quantum computing) and postulates of quantum mechanics As per the definitions qubits were represented as Column Vectors and not row Vectors! What is the reason we ...
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1answer
40 views

What is the apostrophe I see in HEP articles? (NOT antiquark)

I keep seeing references to quarks as q, and antiquarks as qbar, but I'm also seeing things like q' and q'bar. I originally thought it was another form of notation for anti- but it doesn't appear like ...
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3answers
431 views

What is the meaning of external force in the Newtonian force equation?

I came across the following in Goldstein's Classical Mechanics book, section 1.3. In a system of particles, the equation of motion for the $i$'th particle is to be written $$ \sum_j F_{ji}+F_i^{(e)}= \...
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1answer
103 views

What do the overlines above some terms in the Standard Model represent?

Why do some terms in the Standard Model, like the Theta parameter (among others) sometimes have a little dash or bar, like an overline, above them? For example the axion article on Wikipedia mentions ...
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1answer
81 views

Physical interpretation of bra and ket notation mean

I have just started learning quantum computing. The pure state |0> has vector \begin{bmatrix} 1\\ 0 \end{bmatrix} Now what does 1 and 0 indicate about the quantum state ?
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1answer
27 views

Trick for converting equations to and from natural units

Suppose I have an equation, lets say as an example $$E_2=\frac{\sqrt{m^2+M^2+E_1\frac{Mm}{m+M}}}{2}$$ where $m$ and $M$ are masses, $E$'s are energies and this equation is in natural units. Is there a ...
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2answers
161 views

What does it mean to say "tensors transform sensibly"?

I have been reading about tensors and they are described as "objects which transform in a physically meaningful/sensible manner" and obey the equation (for rank 2, but generalises) $T'_{ij}=...
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2answers
40 views

What is $\varepsilon$ in black body curve formula?

I'm currently trying to see the intensity vs wavelength curve for different temperatures using this graphing simulator. However, apart from the temperature and range parameters, there is an epsilon ...
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2answers
47 views

Determining the relations for dimensionless numbers by using their definition

I often see that dimensionless numbers are determined by using their definitions, by the method as shown in the figure: However, I'm having trouble with what is really happening? What does that ...
0
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0answers
53 views

What does $\nabla'$ mean? [duplicate]

In D.J Griffiths Electrodynamics (Page 173) it says, $\nabla' |\vec{x}| = \frac{\hat{x}}{x^2}$. However by my calculation $\nabla |\vec{x}| = -\frac{\hat{x}}{x^2}$ so what does the $\nabla'$ signify?
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0answers
58 views

Significant figures in scientific notation

If I want to express a number in scientific notation, e.g. 0.0068 according to my textbook this is $$6.8 \times 10^{-3}$$ I'm wondering would $$68 \times 10^{-4}$$ be equivalent? 0.0068 has got two ...
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1answer
148 views

SUSY and van der Waerden spinor notation

I am currently trying to read into SUSY and I am running into trouble with the van der Waerden spinor notation for Weyl spinors. I am looking for resources that construct and justify the index ...
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2answers
427 views

Why do physicists like to put the imaginary unit $\:i=\sqrt{-1}\:$ everywhere?

There are many disagreements of convention between mathematicians and physicists, but a recurring theme seems to be that physicists tend to insert unnecessary factors of $i = \sqrt{-1}$ into ...
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1answer
57 views

How does nested powers work?

Sir Roger Penrose has quantified the "very special" nature of the big bang as being "1 part in 10 to the 10 to the 243", but I do not understand what this really means - my ...
0
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2answers
90 views

What is the functional form for a ket vector in the position basis?

$\newcommand{\ket}[1]{|#1\rangle}$ $\newcommand{\bra}[1]{\langle#1}$ This is a question that has long confused me, what is the actual functional form of a ket vector, specifically in the position ...
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2answers
174 views

What is the meaning of $O(10^{-14})$?

What is the meaning of the symbol,O(1),O(10^-4),in the picture above the text box? I am not a computer engineer or a computer language major. Please tell me simply. I don't want an explanation with ...
0
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2answers
96 views

Physical meaning of the exterior derivative of the first law of thermodynamics

We know, $$ dU = d \overline{q} - d \overline{W}.$$ suppose we took the exterior derivative on both sides, then: $$ 0= d( d \overline{q}) - d( d \overline{W})$$ This means, $$ d^2 \overline{q} = d^2 \...
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2answers
81 views

On Dirac notation: inner product vs base representation

The Dirac notation $\langle a | b \rangle$ seems somewhat ambiguous. On one hand, it can be seen as inner product of elements $a(x)$ and $b(x)$ of the Hilbert space $\scr H$, namely: $$\langle a | b \...
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2answers
141 views

Matrix mechanics tensor products in Fock space

In quantum mechanics, bra-ket notation is often used to represent the state vectors of the system. It is also possible to write these state vectors as "actual" vectors, for example if the ...
5
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4answers
710 views

Inner product linearity on Dirac notation

I was starting to learn Dirac notation with MIT's notes on QM. The introduction states that Dirac notation starts from turning inner products from: $$ \langle{u}, v\rangle $$ to, substituting the ...
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1answer
39 views

Integral over momentum space of the distribution function

I have $$\int \frac{d^3p}{(2\pi)^3}p\frac{\partial f}{\partial p} = \int \frac{d^2\hat{p}}{(2\pi)^3}\int^\infty_0 p^2dp\ p \frac{\partial f}{\partial p} ,$$ where $f$ is the distribution function, $\...
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1answer
215 views

What does the notation $H{\parallel}ab$ mean?

In a research paper (Phys. Rev. B 84, 052507 (2011)), I have found the notation $H{\parallel} ab$, where $H$ is an applied magnetic field. In this context $a,b,c$ are the lattice vectors. What does ...
0
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1answer
83 views

The symbol of the constant for $\frac{ 1 }{ 4 \pi \mu_{0} }$ of vacuum permeability

$$ k_{e}=\frac{ 1 }{ 4 \pi \epsilon_{0} } ~~ \leftarrow~~ \text{coulomb constant} $$ I would like to know whether the follwing "constant of permeability" $$ \frac{ 1 }{ 4 \pi \mu_{...
0
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1answer
70 views

Tensor notation of covariant derivative

I'm trying to apply Wald's General Relativity equation $3.1.14$: $$\nabla_a{T^{b_1\dots b_k}}_{c_1\dots c_{\ell}}=\overline{\nabla}_a{T^{b_1\dots b_k}}_{c_1\dots c_{\ell}}+\sum_i{C^{b_i}}_{ad}{T^{b_1\...
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2answers
71 views

What does this symbol represent in circuits?

I was watching a YouTube video on the superposition theorem and came across a symbol : The symbol on the right . He says it's a current source , Is that all it is ? Is there a name to this so that I ...
4
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1answer
81 views

The cross on Feynman diagrams

In figure (a), in the upper part of the loop, What is the meaning of the cross between smuon and the node of selectron and photino?
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0answers
44 views

Unequal forms of the Yang-Mills equation in local coordinates

I found three different expressions for the Yang-Mills equation in local coordinates: In 1: $\square A^{\beta}-\partial^{\beta}\left(\partial_{\alpha} A^{\alpha}\right)+\partial_{\alpha}\left[A^{\...
1
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1answer
75 views

Index convention according to Schwartz

On page 15 of his QFT book, Schwartz writes that all the following contractions are equivalent as long as the flat metric is used: $$v^\mu w_\mu=v_\mu w^\mu=v_\mu w_\mu=v^\mu w^\mu.$$ Isn't this false?...
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2answers
119 views

Do MIT students omit square braces of SI unit? [closed]

$$ v:=\text{symbol which represents a speed } $$ As concrete value of $ v$ is specified, at least the below 2 notations can be done. $$ \text{notation 1} \rightarrow v=10 \left[ \frac{ \text{m} ...
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1answer
39 views

What is $\epsilon$ in the $\delta$ smooth action functional of the Lagrangian?

At the beginning of the Lagrangian Mechanics Wikipedia page, it gives a $\delta$ function on the stationary point of the action $\cal S$: Given the time instants $t_1$ and $t_2,$ Lagrangian mechanics ...

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