Notation Definition and 1000 Threads

Homework Statement Prove or disprove the following (i) ##\forall a\in\mathbb{R}[(\forall \epsilon>0,a<\epsilon)\Leftrightarrow a\leq 0]## 2. The attempt at a solution Can't we disprove the above statement by telling ##a\leq 0 \nRightarrow (\forall \epsilon>0,a<\epsilon)## through a counter...

To express the derivative of a particular function, I have recently come across a "new" notation. For the function x2-3x for example, can you write the derivative operator like this? x2-3x dx . I heard this is called the Euler notation, is it valid?

Edit = Solved. My error. 1- ##\Big( \frac {n_1 +n_2}{n_1} \Big)## in Siegel,S "Nonparametric Statistics" P.153 re. Randomization test for 2 independant samples. eg. ##\Big( \frac {4 + 5}{4} \Big) = 126## Used in calculating number of "equally likely ways" data could have been assigned under H0...

I have been looking through some notes on fermion wavefunction operators and noticed some summations involving indexes repeated 3 times.I know this is not allowed when using the Einstein summation convention. So my question is : is the Einstein convention not used in Quantum mechanics ? and do...

Hello! (Smile) I want to prove or disprove the statement $f(n)+o(f(n))=\Theta(f(n))$. Do I have to set $g(n)=o(f(n))$ and use the definition, that is that $\forall c>0, \exists n_0(c) \in \mathbb{N}$ such that $\forall n \geq n_0: 0 \leq g(n)<cf(n)$ ? (Thinking) Is the following right? We...

"Expanding the taylor series for ##f(x)##.." (See picture) is this a typo? Aren't we expanding ##f(x + \Delta x)##? Also, when we evaluate ##f(x)## (coefficients in the expansion), are we assuming ##\Delta x = 0## by setting ##x + \Delta x## (argument of the function) equal to ##x##? Or are we...

Hey! :o Using vector notation describe a triangle ( in space ) that has as vertices the origin and the endpoints of the vectors $\overrightarrow{a}$ and $\overrightarrow{b}$. Could you tell me what I am supposed to do?? (Wondering)

Suppose two people, X and Y, have two different stopwatches. X starts his/her stopwatch as some particle passes an origin. We can model the velocity of the particle by ##\vec{v}(T)##, where ##T## is the reading on the first stopwatch. After an amount of time ##\Delta t##, Y starts his/her...

i might have been spelling them wrong, but i can't find what do they mean: what's the difference between [psi](x) and [psi tilda](x)? i mean this thingy.. (~) and what's h(bar)? (in the formula p=h(bar)k) [i mean the bar thing] and other stuff.. things that i need to know...? i'm new to the...

I wasn't sure where to post this, and I hope this is the right place. I've been reading ahead of my lectures, and I've gotten a book that introduces tensors. It very quickly introduces Einstein Summation Convention, which I think I understand, \sum_{i=1}^{3} x_{i} y_{i} = x_{i} y_{i} = x \cdot...

Hi! Two exerts from my lecture notes: "Assume we have a system of point masses in position ##\vec{r_i}## which are influenced by forces ##\vec{F_i}##." "Let's say you have a system where ##\vec{F_i} = - \nabla_i V##" In the second line, what does the notation ##\nabla_i## mean? Why is that...

We've just started with this new notation in class and I'm just trying to get a little more insight into the basics so have a few very basic questions if someone here can help? 1) dxμ = (dt,dx,dy,dz) I understand that's it's just a four-vector with four components but, what would dxμ be equal...

What is the notation for the angular distance traveled by an object moving in circular motion? s is for regular distance (m,ft,inches, etc.). What I want is some x to be the distance in either degrees or radians. How should I call that x?

1]express j! in ∏ notation Are they just wanting something like $$j! + (j-1)! + (j-2)! +(j-3)!$$...?

I have been studying quantum physics for some time, yet I still cannot seem to understand the principles behind bra-ket notation (especially how spin states are described and the probabilities/eigenvalues). It would be great if someone could give me a basic explanation and/or maybe recommend...

Homework Statement I've been given the series 3,4,6,10,18... and asked to express as the ∑ar, between r=0 and r = infinity. Homework EquationsThe Attempt at a Solution Well, I can see a pattern! The difference between terms doubles every time. I'm having difficulty expressing this...

Hi, I want to translate this equation R_{\hat{n}}(\alpha)\vec{x}=\hat{n}(\hat{n}\cdot\vec{x})+\cos\left(\alpha\right)(\hat{n}\times\vec{x})\times\hat{n}+\sin\left(\alpha\right)(\hat{n}\times\vec{x}) to index notation (forget about covariant and contravariant indices). My attempt...

I was reading my lecturer's notes on GR where I came across the geodesic equation for four-velocity. There is a line which read: Summing them up, \partial_i g_{aj} u^i u^j - \frac{1}{2} \partial_a g_{ij} u^i u^j = \frac{1}{2} u^i u^j \partial_a g_{ij} I'm trying to understand how LHS = RHS...

I'm trying to apply BRA KET notation to my notes on particle physics. please could someone confirm that the kroneker delta function may be written \delta _{ij} = \left \langle i |j \right \rangle OR would it be written δij = |i> <j| I know i and j are indices, so can BRA KET even be...

Homework Statement (a) Find matrix element ##M_{ij}## (b) Show that ##x^j## is an eigenvector of ##M_{ij}## (c) Show any vector orthogonal to ##x^j## is also an eigenvector of ##M_{ij}## Homework EquationsThe Attempt at a Solution Part(a) [/B] \frac{\partial^2 \Phi}{\partial x^i x^j} =...

1. In Griffiths, in the section where he discusses the 'total' spin of two spin 1/2 particles (''Addition of angular momenta'') he starts of using a notation new to me. Namely ##\chi=\chi_1\chi_2## where I know what ##\chi_1## and ##\chi_2## represent independently, which has been discussed in...

Homework Statement Hey guys. So basically I'm doing some Calc I homework and I'm working on the domain of this function: g(x) = √tan(2x+π) Homework Equations Now to determine the domain, I know that the function under the root cannot be negative. The Attempt at a Solution So after...

Hi there, I am reading an introduction for atomic physics. In one section, it introduces the energy levels for Rubidium and there are some labels like F=1, F=2 etc. shown next to the fine structure of a level . Also refer to...

The problem: The velocity ~v (vector notation, don't know how to type) is given by: ~v = (6.0t - 4.0t^2)ˆi + 8.0ˆj + (3.0t) with |~v| in meters per second and positive t seconds. ˆi, ˆj, ˆk have their usual meanings (unit vector notation). (a) What is the acceleration ~a of the particle when...

Hi, I've come across this notation to describe a composite ply layup: [2/4/4/2] – [45/0/-45/45/90/-45]s I know that the second part is notation for: [45/0/-45/45/90/-45/-45/90/45/-45/0/45] But what is the [2/4/4/2] in referrence to? I have noticed that 2+4+4+2 = 12, and there are 12 ply...

Is there anywhere that teaches tensor analysis in both tensor and non tensor notation, because I'm having to pause each time i look at something in tensor notation and phrase it mentally in non tensor notation at which point it becomes staggeringly simpler. Any help apreciated

My text has: ##\frac{\partial x^{a}}{\partial x^{p}}V^{p}-\frac{\partial x^{a}}{\partial x^{r}}V^{r}+\frac{\partial x^{a}}{\partial x^{p}}T^{p}_{qr}V^{r}+\frac{\partial x^{a}}{\partial x^{p}}\frac{\partial }{\partial x^{q}}V^{p}=\frac{\partial x^{a}}{\partial...

hi! in the first page of the attached pdf, after the title " 't hooft double line notation", he says that we have to consider the gluon as NxN traceless hermitian matrices to convince ourselves about the double line notation. there is my question: if you want the indices a,b to run from 1 to...

Homework Statement (a) Find faraday tensor in terms of ##\vec E## and ## \vec B ##. (b) Obtain two of maxwell equations using the field relation. Obtain the other two maxwell equations using 4-potentials. (c) Find top row of stress-energy tensor. Show how the b=0 component relates to j...

I have a question about function notation as it is used in physics equations. Say that we have the equation $$x = x_{0} + v_{0}t + \frac{1}{2}at^{2}$$ Obviously, x is a variable quantity representing all possible displacement values that are dependent on the value t. But, what happens when...

My notes read that, the quantity ##K^{2}=K_{uv}V^{u}V^{v}## is constant along geodesics, where ##K## is a killing vector. I know my definition that the quantity on the RHS is conserved, I'm just wondering why do we call it ##K^{2}##, rather than anything else? In analogy to a killing vector, if...

I know that a function is typically defined as a mapping such as ##f: x\rightarrow f(x)##, but I am confused about how we really "define" functions. In many common texts, we define functions as ##f(x)##, such as ##f(x) = 2x##. And we say that we take the derivative of a function ##f(x) = 2x## by...

Are these three sets equivalent? $$A=\left\{(x,y):x,y\in\Bbb{R},y\ge x^2-1\right\}$$ $$B=\left\{x,y\in\Bbb{R}:y\ge x^2-1\right\}$$ $$C=\left\{(x,y)\in\Bbb{R}^2:y\ge x^2-1\right\}$$ I am thinking that $A$ and $C$ are, but not $B$ as it might be ambigious as to which dimension it is in, i.e it...

During my reading I met with, (Λ-1)μν = Λνμ ≡ ημρΛρσησν. Is it correct to say that η raises and lowers the indices of Λ giving Λμν, which, in turn, will give (Λ-1)μν = Λμν? Thanks for any help.

Homework Statement When we use ##J^{/pm} ## where ##/pm## gives the parity, some sources say ##J## is the spin and some say the total angular momentum, I'm confused ! Also in my notes we have ##P=(-1)^l##, but looking on this thread...

I've looked around on the internet a bunch, for a standard way to write an arbitrary number of nested functions (eg. ##{f_1}\circ{f_2}\circ\cdots\circ{f_n}##) without ellipses and with a second input variable (eg. the i in ##f_i##), but never found anything. If anyone does this, what is the...

Homework Statement When we write the V_0 on the right of the diagram as show below, between which two points does the voltage drop refer to? There are two nodes on the top correct? I am assuming the voltage drop refers to the two rightmost nodes. I've tried to circle the nodes. See this...

for a degnerate system it's in my notes that you can write: H^{(0)}\Psi _{1}=E_{0}\Psi _{1} H^{(0)}\Psi _{2}=E_{0}\Psi _{2} and (not related) we write the general Schrodinger equation H_{0}\Psi + V\Psi = E\Psi Please could someone tell me what both the upper and lower zeros on the H mean...

Do someone knows what this dot "." means? I just know this notation [001]. Thank u Abigale

In Srednicki's text on quantum field theory, he has a chapter on quantum Lorentz invariance. He presents the commutation relations between the generators of the Lorentz group (equation 2.16) as follows: $$[M^{\mu\nu},M^{\rho\sigma}] =...

Homework Statement Consider a ^3D_X where X=3/2 state. a) What are the possible values of S, L, J and J_z? Homework Equations Spectroscopic notation for this LS coupling is ^YL_J where Y=2S+1. J ranges from|L-S| to |L+S| The Attempt at a Solution Since L=2 and S must be equal to 1, how can...

Homework Statement This is a problem I had as a margin note in an old notebook that I will recycle. I want write it using LaTeX. Problem is that I also want to write it using "proper" math notation instead of English words. Firstly, I got this: \textrm{Proof that }\nexists x, y \in...

HI all, I have the equation, 6x^2-2>9x for which I'm to find the solution set in interval notation. I've rewritten the inequalty as 6X^2-9x-2=0. I tried to factor, but no go. Then I used the quadratic and got 9+/- rad(129)/-18. The answers I get for x are -1.1309 and .1309. The calculator...

Homework Statement How to indicate that a vector b is in the span of the columns of a matrix C? Homework Equations I could type the definition of Span here, but Wikipedia has it too and it is not necessary or useful now. The Attempt at a Solution \mathbf{b} \in \mathrm{Span}\{\mathbf{c}_1...

See the two pages I've attached. 47 and 48. I'm trying to understand the notation used for the (129) equations. A hint is just below the equations. ( ) ∑. These pages are describing the LSQ method. (aa), etc. aa doesn't make sense to me. Herget devised this notation in 1948. Comments

I've been thinking about something recently: The notation d2x/d2y actually represents something as long as x and y are both functions of some third variable, say u. Then you can take the second derivatives of both with respect to u and evaluate d2x/du2 × 1/(d2y/du2). Now I think it's also...

Homework Statement Consider a one-dimensional particle subject to the Hamiltonian H with wavefunction \Psi(r,t) =\sum_{n=1}^{2} a_{n}\Psi _{n}(x)e^{\frac{-iE_{n}t}{\hbar}} where H\Psi _{n}(x)=E_{n}\Psi _{n}(x) and where a_{1} = a_{2} = \frac{1}{\sqrt{2}}. Calculate the expectation value of the...

I know that the metric tensor itself utilizes Einstein summation notation but the field equations have a tensor form so the μ and ν symbols represent tensor information. I'm trying to wrap my head around how Einstein used summation notation to simplify the above field equations but it seems...

These are the notations of quaternions that i have seen: q = s + v q = (s, v) q = s + ai + bj + ck where s, a, b, & c are members of the reals but why not use the notation of: q = (s, a, b, c) isn't it the same as the 2nd notation except it is clearer? So why does it take a quaternion to be...

Homework Statement I am trying to prove $$\vec{\nabla}(\vec{a}.\vec{b}) = (\vec{a}.\vec{\nabla})\vec{b} + (\vec{b}.\vec{\nabla})\vec{a} + \vec{b}\times\vec{\nabla}\times\vec{a} + \vec{a}\times\vec{\nabla}\times\vec{b}.$$ I can go from RHS to LHS by writng...