Notation Definition and 1000 Threads

Alright, so I was wondering if anyone could help me figure out from one step to the next... So we have defined |qt>=exp(iHt/\hbar)|q> and we divide some interval up into pieces of duration τ Then we consider <q_{j+1}t_{j+1}|q_{j}t_{j}> =<q_{j+1}|e-iHτ/\hbar|q_{j}>...

Homework Statement 2n-1 Sigma (3i+1) = n(6n-1) i=0 prove for all positive n Homework Equations The Attempt at a Solution It holds true for n=1 5=5 then P: m+1 2m+1 Sigma(3i+1) = (m+1)(6(m+1)-1) or 6m^2 + 11m + 5 i=0 then 2m+1 Sigma(3i+1) = m(6m-1) +...

Hello, In the notation adopted by Peskin and Schroeder, the single particle state is \left|\boldsymbol{p}_1, s_1\right\rangle = \sqrt{2 E_{p}} {a_{p_1}^{s_1}}^{\dagger}\left|0\right\rangle How does one write down \left\langle r|\boldsymbol{p}_1, s_1\right\rangle = \sqrt{2 E_{p}} \left\langle...

Homework Statement Homework Equations The question is related to Riemann Sums The Attempt at a Solution I can not understand the notation of the question. Can someone explain the question to me. Or solve the question, i will understand it myself. Thanks

I was looking at an answer regarding resistors, and saw the notation; R = R1 + R// where 1/R// = 1/R2 + 1/R3 I was wondering what the two parallel lines after the R indicate? Thanks.

Homework Statement http://quantum.leeds.ac.uk/~almut/section2.pdf Please note i am referring to the above notes I basically don't get how the maths works to get (eq(25))(eq(22))(eq(24)) = eq(26) am i missing something interms of the commutator relations ? Homework Equations The Attempt at a...

Homework Statement I'm having a hard time understanding when we approximate higher order powers by order notation, especially when it comes to working out the Truncation Error for Finite Differences. My notes say "We use the order notation O(h^{n}) and write X(h) = O(h^{n}) if there exists a...

Homework Statement find each of the angular momentum quantum numbers and the spectroscopic notation of the ground state electron configuration. Homework Equations n2s+1L J The Attempt at a Solution so for "each of the angular momentum quantum numbers" I am just finding the L in...

I am new to quantum physics. My question is how to write the Hamiltonian in dirac notation for 3 different states say a , b , c having same energy. I started with Eigenvaluee problem H|Psi> = E|psi> H = ? for state a? SO it means that indvdually H= E (|a><a|) for state a and for all three...

Hi, i am evaluating the integral \int_{-\infty}^{+\infty}dE \langle p'|E \rangle \langle E| e^{-iEt/ \hbar} |p\rangle However, i am unsure how to evaluate \langle E| e^{-iEt/ \hbar} |p\rangle . I am not sure if it is simply e^{-iEt/ \hbar} \times \langle E|p\rangle or something else. Any...

Homework Statement This is not a homework question, but rather a review question. I have the answer, ill post below, but have no idea how to get to the answer :) Question: "A constant force of 90.0N acts on a ball while it has a displacement of 1.40m at 10 degrees below the x-axis. The...

Homework Statement a) nƩr2(r-1)r=1 Homework Equations Using the summation series formulae... The Attempt at a Solution So far I have got: r2(r-1) = r3-r2 Ʃr3 = \frac{1}{4}n2 (n+1)2 Ʃr2 = \frac{1}{6}n(n+1)(2n+1) Therefore, Ʃr3-r2 = \frac{1}{4}n2 (n+1)2 -...

Hi, I am very new to general relativity and have only just started to learn how to do some very basic manipulation of tensors. I can understand the methods I am using and have some idea of what a tensor is but am not sure what the difference between upper and lower indices signifies. I can...

The notations are: W^+, W^-, and Z^0. I'm assuming the W stands for Weak. But, why Z for the neutral one? Is there even a reason?

Homework Statement I'm sure this is quite simple, but I don't understand the notation. This is from a supplemental book that we have to do outside of class--there isn't a matching textbook and I really don't understand what they want here. Homework Equations I noticed that if i square...

Homework Statement For the infinite square well, a particle is in a state given by \psi = \frac{1}{\sqrt 2}(\psi_1 + \psi_3) , where \psi_1 and \psi_3 are energy eigenstates (ground state and the second excited state, respectively). Represent this state as a column matrix \psi> in...

Homework Statement I have the state: |\psi>=cos(\theta)|0>+sin(\theta)|1> where \theta is an arbitrary real number and |\psi> is normalized. And |0> and |1> refer to the ground state and first excited state of the harmonic oscillator. Calculate the expectation value of the Hamiltonian...

What is meant by things like: R_{[abc]} and also things like: \nabla_{[a\nabla_b]} Where you have square brackets in the subscript? Thx

Ok, I'm not very familiar with set notation. I was just wondering if the following is correct notation and means what I think: {x\inS : \existsy\inx, y\inW} S is a set of pairs of symbols (tuples of length 2 is the technical term I believe). W is a set of symbols. What I want is the...

Hello all, I'm in the process of simplifying the following equation using one-point rule and other predicate logic. But I’m a bit stuck with where to start or which inference rule to use first. Please help or any pointers would be much appreciated. Thanks

Hi ! What does the notation mean exactly when a function has power minus one ? For example i have seen the logistic function written as: f(x) = f0[1 + exp(−βx)]^-1

Can someone explain to me how Cov(x,y)=[X-E(x))(Y-E(y)] and this would equal 0 under the normal OLS assumption. I know how to calculate the covariance, but X here is a matrix. So I don't understand the logic of this formula...

Homework Statement We have a capacitor in parallel with an inductor. These are both in series with a resistor and capacitor. Calculate the J notation Impedance of the network. I only want the initial basic solution. The problem I have is that sometimes the J notation of C is -ve and...

Hi all, I was diving into my 3rd year quantum assignment and I saw the following which I have to use for the rest of the question to prove the Cauchy-Schwarz inequality: Homework Statement || a|x> + b|y> ||^2 I only really learned a bit about Dirac notation last year, so please...

While discussing Taylor's theorem, my professor pointed out that for n=2, Taylor's Theorem says: f(x) = f(x_{0}) + f'(x_{0})(x - x_{0}) + O(|x - x_{0}|^{2}) He then emphasized that O(|x - x_{0}|^{2}) is a much better approximation than o(|x - x_{0}|). But how is O(|x - x_{0}|^{2}) a...

I'm trying to decipher exactly what it means to say the following things: (1) The ground electronic state of NO_2 is ^{2}A_1; (2) The ground electronic state of ClO_2 is ^{2}B_1; (3) The ground electronic state of O_2 is ^{3}\Sigma^{-}_g. I really don't have a clue what these symbols...

This is just me being pedantic :)

Homework Statement http://people.math.carleton.ca/~mezo/A5math1102-11.pdf number one Homework Equations The Attempt at a Solution What does Z5/5 mean?

Homework Statement Normalised energy eigenfunction for ground state of a harmonic oscillator in one dimension is: 〈x|n〉=α^(1/2)/π^(1/4) exp(-□(1/2) α^2 x^2) n = 0 α^2=mω/h suppose now that the oscillator is prepared in the state: 〈x|ψ〉=σ^(1/2)/π^(1/4) exp(-(1/2) σ^2 x^2)...

I'm trying to figure out what the summation notation of (1-x1)^θ * (1-x2)^θ * ...(1-xn)^θ would be for summation I know I need to convert this to a summation notation in order to solve my problem, but I can't figure out how to convert it. Any help will be appreciated.

Is there any standard (or reasonably standard) notation for the following function? Basically, it's ∏(n) - ∏(n-1) or, which is the same thing, \frac{\Lambda(n)}{\log n} (where ∏(n) is the Riemann prime counting function and \Lambda(n) is the Von Mangoldt function) Basically...

Not a particularly direct question, just something I don't mathematically understand and would very much appreciate help with. For some scalar field \phi, what would \partial_{\mu} \phi^{*}\partial^{\mu} \phi mean in mathematical terms. ie how would I calculate it? From what I understand...

Homework Statement Show that \nabla \times (a \cdot \nabla a) = a\cdot\nabla(\nabla\times a) + (\nabla \cdot a(\nabla \times a) - (\nabla \times a)\cdot \nabla aHomework Equations \nabla \times (\nabla \phi) = 0 \nabla \cdot (\nabla \times a) = 0 The Attempt at a Solution I started with...

If you look here http://planetmath.org/encyclopedia/RiezsLemma.html , there seems to be something missing - nothing is said about the norm of (x_alpha) or about the norm of (s - x_alpha). Now, the same thing seems to happen here...

I'd like to go over my approach to a question I am doing right now, but I've posted my general approach instead of the question itself. Say there is some object with three forces acting on it, and these forces are given to me in vector notation (i.e. with unit vectors "i" and "j"). I am also...

Homework Statement Show that \left\langlex|p|x'\right\rangle = \hbar/i \partial/\partialx \delta(x-x') 2. The attempt at a solution \left\langlex|p|x'\right\rangle = i\hbar \delta(x-x')/(x-x') = i\hbar \partial/\partialx' \delta(x-x') = \hbar/i \partial/\partialx \delta(x-x') For...

Is Tab\partialcf = Tac\partialbf, where T is a tensor? Seems to me like you should be able to do this: Tab\partialcf =Tab\deltabc\partialbf =Tac\partialbf Maybe I'm using the Kronecker delta incorrectly. Could someone check this for me?

Hello, why is <j' m' | j m>=0 if j \not= j' \; \text{or} \; m \not= m' j and m are describing states. I don't understand why an 'empty bracket' behaves like that.

What is the meaning of \frac{\partial F(x)}{\partial(\partial f(x)/\partial x)} in which a derivative appears in place of the variable x in the denominator? Anyone, please?

I have seen in various locations different conventions regarding the location of a prime symbol denoting a tensor represented in a new frame. For example, if the position four-vector is x^{\mu} then this four-vector in a different frame is often written as either x'^{\mu} or...

Homework Statement Consider scalar functions u = u(x). Compute the gradients ∇u for: u(x) = (x, y, z) u(x) = (y, z, x) u(x) = (x^2y, 10, z + x) Homework Equations This is a question on my homework for undergraduate Fluid Mechanics. The teacher has been assigning math problems in topics...

Hi there, I'm writing a research paper and have hit a roadblock, (wikipedia did not help) and one of my collaborators sent me an e-mail that I do not understand. I am attempting to find when the following functional is stationary: T = \int\limits_{\lambda_{1}}^{\lambda_{2}}...

Homework Statement Two diamonds begin a free fall from rest from the same height, a time "delta t" apart. How long after the first diamond begins to fall will the two diamonds be a distance "d" apart? Give your answer in terms of the variables given and "g". ( Solve for t= ) Homework...

Homework Statement Draw the following vector. Label the angle that specifies the vector's direction, then find its magnitude and direction. Homework Equations vector a = 2.0i - 6.0j The Attempt at a Solution I get stuck here: I don't know which angle to use.

Hello, i am a beginner in quantum mechanics and i have those basic questions on the bra-ket notation: Which dimension has a ket | \phi > describing a state normally? Maybe \quad C ^n? Which dimension has a bra-ket <\psi | \phi >then? Maybe \quad C ? How do you get the matrix...

"set builder" notation and proofs I'm curious about the references to "set builder" notation that I see in forum posts. Is this now a popular method of teaching elementary set theory and writing elementary proofs? I haven't looked at materials for that subject in the past 20 years. The...

Homework Statement Add (9.8x10^3s)+(9.9x10^4s)+(0.017x10^6s) Homework Equations None The Attempt at a Solution I have entered 125800, as well as 1.26x10^5 but the website marked both of those wrong. I've done this problem every way you could do it I think and it comes out to the same answer...

Homework Statement #5 and #6 of the attached pdf on page 5 (graph on page 4 relates to said problems) Note: The professor did not cover how to do a problem like this, and the book does not have a similar problem, nor any other handouts. This definitely was a unique question. I'm unsure if I...

Homework Statement Consider the following vectors: a = (5.0m) i + (2.0m) j b = (-14m) i + (6.0m)j Sum of a+b in unit vector notation? Homework Equations The Attempt at a Solution I'm not sure about this notation, all I know about adding vectors is graphically. Does (5.0m)...

(x∈R → f(x)>0) → f is asmani. What does it mean: 1. If there exists some x in R such that f(x)>0, then f is asmani. 2. If for all x in R we have f(x)>0, then f is asmani. 3. It's ambiguous or meaningless. 4. ...? Thanks in advance.