Notation Definition and 1000 Threads

A ##\frac{df}{dx}## notation is problematic. Obviously, the letter 'd' has very different meaning when applied to the function or to the argument. Additionally, a separate letter '##\partial##' is used to denote a partial differential (a very rare case in math when a notation used for a general...

It's said that every ket has a unique bra. For any vector ##|v> ∈ V## there is a unique bra ##<v| ∈ V*##. I'm not sure what that means. What is unique? Can anyone please help me understand. Thank you

As a follow up from my other thread, where I consider popular media describe entanglement sort of as: and I think this may be wrong. As a follow up question I want to put forward this: A singlet state of entangled particles is notated in a superposition of product states as: ##|up, down...

(This is not about independence of ##q##, ##\dot q##) A system has some holonomic constraints. Using them we can have a set of coordinates ##{q_i}##. Since any values for these coordinates is possible we say that these are independent coordinates. However the system will trace a path in the...

Hello : i am reading now landau & lifshitz book on mechanics and i have small question : about L(v^2) notation it was not very clear in the book and i couldn't understand it correctly anyone can explain it or provide a link with explanation page (4 - 5) Best regards Hagop

Homework Statement:: Write each of the following sets in set-builder notation. Relevant Equations:: None. {2, 4, 8, 16, 32, 64...} =2·{1, 2, 4, 8, 16, 32...} What should be the next step in this work?

What does ##S=\partial V## and ##C=\partial S## signify, usually I have only seen books writing ##C## when evaluating a line integral over a curve ##C## and ##S## when evaluating a surface integral over a surface ##S##. Could someone clarify what ##\partial S## and ##\partial V## mean?

Summary:: Operator acts on a ket and a bra using Dirac Notation Please see the attached equations and help, I Think I am confused about this

I saw it somewhere but I did't know exactly what it meant. Could someone explain it to me like I am 5? Does it mean we integrate with respect to x n times? $$\int_{\mathbb{R}^n}f\, \mathrm{d}^n x$$

Does $$\partial^\beta(g_{\alpha\beta}A_\mu A^\mu)$$ mean the same as $$\frac {\partial (g_{\alpha\beta}A_\mu A^\mu)}{\partial A^\beta} ?$$ If not could someone explain the differences?

Dear PF Forum, I watched this video 10 ^ 10 ^ 10 ^ 5600 The narative says, It is 1 followed by 5600 zeros But that's not what I think, I think it is 1 followed by I don't know. What does this number means? Is it A: 10 ^ (10 ^ (10 ^ 56))) or B: ((10 ^ 10) ^ 10) ^ 56? It says that "As...

My attempt: ## ( \rightarrow ) ## Suppose G is injective. Let ## y \in Y ## be arbitrary, denote A = ## \{ y \} ## so that ## G(A) = G(\{ y \}) = f^{-1}[\{ y \}] = \{ x \in X | f(x) \in \{ y \} \} =\{ x \in X | f(x)= y \} ##. [ However, now I am stuck because I don't know if ## G(A)=...

I found the following functions ( In lambda notation ) to be injective, and now I am trying to find the inverse functions for them ( the inverse for the Image of ## f ## ) but I am stuck and I need help: 1. ## f = \lambda n \in \mathbb{N}. (-1)^n + n^2 ## 2. ## f = \lambda g \in \mathbb{R}...

Hi. Newbee question. What does the notation V^G mean where V is a vector space and G is a group? I found it in: A linear algebraic group G is called linearly reductive if for every rational representation V and every v in V^G \ {0}, there exists a linear invariant function f in (V^*)^G such that...

[Moderator's note: Thread spun off from previous thread due to topic change.] This thread brings a pet peeve I have with the notation for covariant derivatives. When people write ##\nabla_\mu V^\nu## what it looks like is the result of operating on the component ##V^\nu##. But the components...

Hi all, I am having some problems expanding an equation with index notation. The equation is the following: $$\frac {\partial{u_i}} {dx_j}\frac {\partial{u_i}} {dx_j} $$ I considering if summation index is done over i=1,2,3 and then over j=1,2,3 or ifit does not apply. Any hint on this would...

This is probably kind of dumb, but it's really bothering me for some reason. I originally saw traveling wave solutions to the wave equation as ##f(kx−\omega t)## for right traveling (as t gets bigger, x needs to be bigger to "match" it's previous value) and ##f(kx+\omega t)## for left-traveling...

In the days when scores were written by hand, how were parts for drums written? It's clear that ordinary notation is sufficient to indicate the duration of dumb beats - although writing each beat for a drum would be tedious. Was there some system of abbreviation? Did composers attempt to...

I can't why there are four elements in each ket instead of only two

Hi, Just a quick question about conditional and marginal probabilities notation. Question: What does ## p(a|b, c) ## mean? Does it mean: 1) The probability of A, given (B and C) - i.e. ## p[A | (B \cap C)] ## OR 2) The probability of (A given B) and C - i.e. ## p[(A | B) \cap C] ## I was...

Hello (again). I have become quite familiar with the dot notation in Python. The dot "operator", assuming operator is the right term, seem to have many uses. For example: 1) After an instance name, it can be used to access instance attributes and apply instance methods to the object/instance...

I'm working on the time-dependent Schrodinger equation, and come across something I don't understand regarding notation, which is not specific to TDSE but the Schrodinger formalism in general. Let's say we have a non-trivial potential. There is a stage in the development of the TDSE where we...

I get 2^5 x 3^80 Am I correct?

Hi, I'm currently a Grade 11 student and I need help for this question (Precalculus): If $\sum\limits_{i=1}^{50} f(i)=90$ and $\sum\limits_{i=30}^{50} g(i)=60$, what is the value of $\sum\limits_{i=1}^{50} (7 g(i)-f(i)+12)/(2)$? P.S. To those who could answer this, it would be a great help...

Shankar Prin. of QM 2nd Ed (and others) introduce the inner product: <i|V> = vi ...(Shankar 1.3.4) They expand the ket |V> as: |V> = Σ vi|i> |V> = Σ |i><i|V> ...(Shankar 1.3.5) Why do they reverse the order of the component vi and the ket |i> when they...

I am struggling with tensor notation. For instance sometimes teacher uses \Lambda^{\nu}_{\hspace{0.2cm}\mu} and sometimes \Lambda^{\hspace{0.2cm}\nu}_{\mu}. Can you explain to me the difference? These spacings I can not understand. What is the difference between...

ok, by direct substitution i know that either ##x=2## or ##x=4## but i would like to prove this analytically, would it be correct saying, ##xln 2= 2ln x## ##xln_{2}2=2 ln_{2}x## ##x=2 ln_{2}x## ##\frac {1}{2}=\frac { ln_{2}x}{x}## ##ln_{2}x^{1/x}##=##\frac {1}{2}## →##2^{1/2}##=##x^{1/x}##...

Is there a book that emphasizes performing calculations with tensors in modern notation?

In the notation of Function ---> f(x)=y Here f represents the function and x is the variable in the function. we read f(x) as "f of x"or "function of the variable x" what does "function of x " mean that we read ? in this notation what does round brackets ()...

I found some parts of Vol II, Chapter 25 basically unreadable, because I can't figure out his notation. AFAICT he's using a (+,-,-,-) metric, but these equations don't really make any sense: The first one is fine, and so is the second so long as we switch out ##a_{\mu} b_{\mu}## for ##a_{\mu}...

Given a crystal basis ##\{\vec{a}, \vec{b}, \vec{c} \}##, the two lattice vectors ##\vec{r}_1 = u_1 \vec{a} + u_2 \vec{b} + u_3 \vec{c}## and ##\vec{r}_2 = 2u_1\vec{a} + 2u_2 \vec{b} + 2u_3 \vec{c}## both obviously point in the same direction whilst ##\vec{r}_2## is twice as long as...

In the 3rd edition of the Introduction to Quantum Mechanics textbook by Griffiths, he normally does the notation of the expectation value as <x> for example. But, in Chapter 3 when he derives the uncertainity principle, he keeps the operator notation in the expectation value. See the pasted...

As per the image, I am supposed to select all the valid statements. Apparently I'm only partially correct, and so I took another look at the statements. I believe the third statement is wrong, since $$c * (a_m*a_{m+1}*a_{m+2}*...*a_n)$$ =/= $$ (c*a_m)(c*a_{m+1})(c*a_{m+2})*...*(c*a_n)$$ Thus...

Today the inexact differential is usually denoted with δ, but in a text by a Russian author I found a dyet (D-with stroke, crossed-D) instead: In response to my question to the author about this deviation from normal usage, he stated that this was a suggestion from von Neumann. (Which of course...

For the first one so far I have (3 · a + 5 · b)[a, b ≔ b, a] =⟨ Substitution ⟩ (3 · b + 5 · a) So far this is right, however I don't really know the difference between the others. For the second one I did (3 · a + 5 · b)[a ≔ b][b ≔ a] =⟨ Substitution ⟩ (3 · b + 5 · b) For this one I got it...

Mentor note: Moved from a technical section, so is missing the homework template. Hi, I'm always not sure how to prove something in math and I'm wondering if this is enough. ##\vec r \cdot (\vec u + \vec v) ## ##\vec u + \vec v = (u_1+v_1, u_2+v_2,u_3+v_3) = \vec s## ##\vec r \cdot (\vec u +...

hi i am recently following the nptel course in quantum mechanics (The Course ) and it seems like a really good course , but i can't find the book that it based on . my question is : had anyone saw that course before to suggest a QM book related to it ? - she began by an introduction to vector...

If we have the wavefunction ##|ab \rangle##, what do the a and b stand for? In particular, do a and b signify an outcome of some pending or possible measurement, or do they signify some aspect of the wavefunction, and if so, which aspect?

is it true that vectors are symbolised as an italic boldface 'a'

I have a (trivial) question regarding summation notation in Quantum mechanics. Does ∑cnexp(iknx) = Ψ(x) imply that n ranges from -∞ to +∞ (i.e. all possible combinations of n)? i.e. n ∞ ∑exp(iknx) -∞ I believe it does to be consistent with the Fourier series in terms of complex exponentials...

Firstly, apologies for the latex as the preview option is not working for me. I will fix mistakes after posting. So for ##<x>## = (##\sqrt{\frac{\hbar}{2m\omega}}##) ##(< \alpha | a_{+} + a_{-}| \alpha >)## = (##\sqrt{\frac{\hbar}{2m\omega}}##) ##< a_{-} \alpha | \alpha> + <\alpha | a_{-}...

I have a question on formula (3.1) and (3.2) in Feynman Lectures on Physics III 3-1, available online, https://www.feynmanlectures.caltech.edu/III_03.html <x|s> here can be interpreted also as inner product of bra <x| and ket |s>, following usual Dirac notation ? For example, ##<r_1|r_2>## in...

What does the symbol ##\supset## mean as used in equations (3.1) and (3.2) of https://arxiv.org/pdf/1701.07427.pdf

Hi all, The killing vector equation reads: ##\nabla_{(\mu K_{\nu})} = 0## What do the parenthesis mean explicitly? Moreover, I know that ##\nabla_\mu x^\nu = \partial_\mu x^\nu+ \Gamma_{\rho \mu}^\nu x^\rho## So if the parentheses mean symmetric the Killing equation will read...

Functions defines on the plane $\mathbb{R}^2$ or open subsets , using $X=(x_1,x_2)\in\mathbb{R}^2$ asthe coordinates Find all $\alpha \in \mathbb{R}$ such that $(\ln x_1)(x_2^2+x_2)=O(||X||^{\alpha})$ as $||X||\to 0$. and $|X|| \to \infty$ (note that $x_1>0)$

On Page 406 of Nolting Theoretical Physics 1 he has the following notation for the Jacobian determinant $$\frac{\partial( x_{1}, x_{2})}{\partial (y_{1}, y_{2})} = \begin{vmatrix} \left (\frac{\partial x_{1}}{\partial y_{1}} \right )_{y_{2}}& \left ( \frac{\partial x_{1}}{\partial y_{2}}...

Bartlett’s Calculus Paper Reviewed in Mathematics Magazine https://mindmatters.ai/2020/03/bartletts-calculus-paper-reviewed-in-mathematics-magazine/

Looking at. <psi|AB|theta>, under what conditions would this be equal to <psi|A|theta> * <psi|B|theta> I’m just getting into perturbation theory and am running into confusing notation. Thanks john

Hi guys, I am currently having some difficulties with this quantum state. I don't entirely understand what that letter 'i' means, where it comes from and why it appears in brackets [1, i]. Shouldn't there be a '0' instead? I am an absolute beginner in quantum computation. I've been following a...