Formula Definition and 1000 Threads

I've been reading through a derivation of the LSZ reduction formula and I'm slightly confused about the arguments made about the assumptions: $$\langle\Omega\vert\phi(x)\vert\Omega\rangle =0\\ \langle\mathbf{k}\vert\phi(x)\vert\Omega\rangle =e^{ik\cdot x}$$ For both assumptions the author first...

Homework Statement $$ln(x^2)=4$$ Homework Equations ##a^{log_a(x)}=x## ##log_a(a^x)=x## The Attempt at a Solutionln(x^2)=4 <=> ##2ln(x)=ln(4)## <=> ##ln(x)= [ln(4)]/2## <=> ##log_e(x)= [ln(4)]/2## <=> ##e^{ln(4)/2}=x## <=> ##[e^{ln(4)}]^{1/2}## <=> ##sqrt(e^{ln(4)})##...

Homework Statement I am trying to wrap my head around what it means to find an explicit formula for the sequence of partial sums. Question: Find an explicit formula for the sequence of partial sums and determine if the series converges. a) sum from n=1 to n=infinity of 1/(n(n+1)) Homework...

Is this answer is proper? Propane is a natural component of natural gas and is removed during the refining process. Most gas appliances can be converted from one fuel to the other by changing the burners on a stove or changing or adjusting a gas regulator located inside the appliance according...

Homework Statement I need help when changing the formula of the yellow circled part to red-circled part ... Homework EquationsThe Attempt at a Solution I tried , but i didnt get what the author got ... Here's my working ... Which part of my working is wrong ?

Greetings, I am trying to learn more about Rayleigh scattering. I'd like to be able to calculate the amount of light scattered away from a beam as it travels through a volume of gas. So, I checked out the Wikipedia article: http://en.wikipedia.org/wiki/Raleigh_scattering I am not sure I...

Consider a system with a time-dependent Hamiltonian. We know that the evolution of the state of this system, is given by ## \displaystyle |\Psi(t_1)\rangle=T \exp\left( -i \int_{t_0}^{t_1} dt H(t) \right) |\Psi(t_0)\rangle ##. Do you think you can prove that the path integral formula for the...

Had to find the general formula for the gradient of a function r^n. r is the length of the vector connecting (x,y,z) with (x',y',z') I took the gradient of r^n and simplified it. If I plug in any number for in in r^n and go through the process, I will get the same result as if I take this...

Homework Statement Can someone explain why for the first derivative 3 point forward difference formula is 4f(x-h) - f(x-2h) ?? Homework EquationsThe Attempt at a Solution Why it's not f(x-h) - f(x-2h) ? Is there anything wrong with the notes ?

Homework Statement A colony of ants will grow by 12% per month. If the colony originally contains 2000 ants how long will it take for the colony to double in size? Answer - 6.12 months Homework Equations A = P(1+r/n)nt The Attempt at a Solution r = 12% = 0.12 n = 12 P = 2000 A = 4000 t = ...

Homework Statement For the theta series given by : ##\theta(t) = \sum\limits_{n\in Z} e^{2\pi i n^2 t} ## in 1-d there is the transformation formula: ##\theta(-1/4t)=\sqrt{-2it\theta(t)}## To prove this one uses the fact that this theta function is holomorphic and so by Riemann theorem it is...

I'm a Physics undergraduate at University and in my labs module I had to recreate the Rutherford Scattering experiment. The basic setup was similar to this: My problem is that this setup only records data in one plane and not 3D. In reality the particles are scattered in a sort of cone...

I was thinking off building a drone and I was just curious about what the amount of thrust we need to be in order to hover based on weight

I'm reading the path integral chapter of Schwartz's "Quantum Field theory and the Standard model". Something seems wrong! He starts by putting complete sets of states(field eigenstates) in between the vacuum to vacuum amplitude: ## \displaystyle \langle 0;t_f|0;t_i \rangle=\int D\Phi_1(x)\dots...

Homework Statement I would like to show that if ##p(x) = \sum_{i=1}^m a_i x^i## and ##q(x) = \sum_{j=1}^n b_j x^j##, then ##p(x)q(x) = \sum_{k=0}^{m+n} \left( \sum_{i+j=k} a_i b_j \right) x^k##, where the polynomial ring is assumed to be commutative. Homework EquationsThe Attempt at a Solution...

How do I use the double angle identity in order to derive this expression: cos6(u)?

Hello all. I am working on proving some theorems about Monte Carlo simulation and have proven a theorem that, in a certain formula, it is valid to replace a random variable in the denominator of a fraction by its expected value. I have been wondering whether this result can be generalised to...

Working through Leonard Susskind's book The Theoretical Minimum, I noticed an issue with his expansion for the Binomial Expansion (he was missing factorials in the denominators). This led me to some confusion about the final term that is generally written (bn). (a+b)n = an + nan-1b + n(n-1)/2...

Homework Statement A 5-foot long cylindrical pipe has an inner diameter of 6 feet and an outer diameter of 8 feet. If the total surface area (inside and out, including the ends) is k*PI , what is the value of k? Homework Equations In my view the formula should be: 2* PI * radius * h + 2*PI *...

Homework Statement Simplify cos^2 8x - sin^2x Homework EquationsThe Attempt at a Solution I thought it would be in the format of cos2x But I can't seem to figure it out I tried cos (4 * 2x) And I tried to change the sin^2x into 1-cos^2x and I could get any farther. Not sure how else to...

Homework Statement I'm trying to formulate a formula based on an experiment I did. Homework Equations The Attempt at a Solution [/B] where x_1 = mean (one of 5 mean values) x_i = value of variables (there are 4 of them added together) n = number of variables My problem is, for the left...

Homework Statement http://prntscr.com/dcfe0u Homework EquationsThe Attempt at a Solution So I'm not really strong in proofs but I think you may be able to do something like this:$$lnL = \frac{ln(1+1/x)}{x}$$ $$lnL = \frac{1/x^2}{1+1/x}$$ and then more simplifying I get something like: $$lnL =...

So I've been investigating the magnus effect for I guess 2 weeks, but I've not been able to find a formula that would seem to be the correct formula. I did find some formula, but I have my doubts about the completeness/correctness of all of these formulas. Note that I am trying to simulate what...

Homework Statement No actual work, could just use some assistance in understanding formulas involving the centroid of an object, specifically with integrals. For example, how would you understand the following formula(s) (as seen in part 2)? I understand that the centroid is the sum of all the...

I have seen many instances of molecular formulas of two or more compounds with a dot between two adjacent molecular formulas like CuSO4.10H20, CaCO3.MgCO3, K2SO4.Al2(SO4)3.24H20 and so on. What does the dot indicate?

1) How many stages are in N numbers for a FFT? I know N=8 has 3 stages and N=4 has 2 stages ? 2) The DFT formula converts a signal from the time domain into the frequency domain. Is this done by comparing x[n] against signals known as sinusoidal basis functions? are e-j2 pi kn/N sinusoidal...

What happen if i put r=0 into the formula F=(k)mm/r^2 So 1/0=infinity ? then F= infinite large in mathematical sense? is that statement correct ? thank

$\tiny{242.13.3}$ $\textsf{1. Using the known series expansion of $\displaystyle e^x = \sum_{n=0}^{\infty}$, find the series representation of}\\$ $\textsf{a. $e^{-3x}$}\\$ $\textsf{b. $e^{x^3}$}$

Homework Statement I want to reproduce the following matrix: A= [1 -1 0 0 -1 2 -1 0 0 -1 2 -1 0 0 -1 1 ] What i want is to reproduce the second and third row with the formula -x(i+1) + 2x(i) -x(i-1) = 0 This is a coupled oscillation system of N masses (hanging in a rope). The first row...

Homework Statement A skateboarder at a skate park rides along the path shown in (Figure 1) .If the speed of the skateboarder at point A is v=1.3m/s, what is her speed at point B? Assume that friction is negligible. Homework Equations ui+ki=uf+kf u=mgh k=1/2mv2 The Attempt at a Solution...

in Cardano's cubic formula. when reducing a cubic to its depressed form: from ax^3 + bx^2 + cx + d = 0 to a form like y^3 +py + q = 0. what is the motivation behind making x = y - b/3a first before proceeding to depress the cubic? what was cardano's motivation for that substitution or whoever...

Say that we have a sequence defined by the mth degree polynomial, ##a_n=\displaystyle \sum_{k=0}^{m}c_kn^k##. I found the following formula which is a recursive representation of the same sequence: ##\displaystyle a_n =\sum_{k=1}^{m+1}\binom{m+1}{k} (-1)^{k-1}a_{n-k}##. I'm curious as to why...

I recently posted a question on similar line and got few good explanations as well. Still, I am unable to understand clearly. Hence I am going more specific this time. In the given picture taken from internet, friction force acting between an inclined plane and an object is defined as Fr = W x...

Homework Statement given : i need to find the trajectory formula Homework Equations i'm not sure if to use : The Attempt at a Solution [/B] I tried different options with the trigonometric identities that I have written before: thanks

1. Rearrange the following equation 2/(x-2) + 2/(x+2) = 1/2 into the form Ax2+ Bx + C = 0 I did it and got -x2 + 8x + 4 = 0 Am I correct please?

Homework Statement In this notes , why the shear force used is the 19.5kN ? Why not 6.5kN ? From what i know , the formula of shear stress is tau = VQ/ It , where V is the shear force ... There are two values of V in this question , why the larger one (19.5kN ) is chosen ?Homework EquationsThe...

Derive a reduction formula for the integral: $\int \sec^nx dx, \;\;\; n \ge 2.$ - without any help from an online integrator.

So I'm trying to understand something about the Hulse Taylor Binary. Here they talk about the change in periode that actually changes with the period. So what does Pt mean here? And what is actually being explained? P1year also makes no sense to me. Is that the period after one year? And what...

I'm confused about how the predictions of this graph were formed. I have this formula: But the change in frequency per second is about : 2x 10^-12 which has a problem because when you multiply this by 10 years you don't even get a change of frequency of 1/1000 of a second and in the graph it...

Homework Statement In the first photo , i was told that the I represent the moment of inertia about the neutral axis ... But , in the 2nd photo , i found that the author calculate the moment of inertia about the x-axis (parallel to neutral axis ) and y -axis ( perpendicular to neutral axis) ...

What formula can I use to calculate the force I need to apply to a sliding arm that makes a point contact along the edge of a rotating arm attached to a shaft driving a load in order to push the rotating arm to rotate the shaft? The rotating arm is 1 cm wide. The load at the shaft is 1 Nm...

Hello, I am working on a Project and it has been a while since i did calculations With mechanics. The pool would be made in glassfibre with polyester and will be: L=2000mm W= 1750mm h= 400mm we use the E-module for glass, so we use E= 70 000 N/mm2 I= bh3/12 = 2000mm x 4003 mm /12 = 1,067 x...

Homework Statement Develop aprogram that will determine the second derivative of pi(16 x^2 - y^4) at y=2 with step sizes of 0.1, 0.01, 0.001…. until the absolute error (numerical-analytical) converges to 0.00001. Use the 2nd order Central Difference Formula. User Input: y, tolerance Output: h...

$\tiny{242.10.3.27}$ evaluate $$S_j=\sum_{j=1}^{\infty}3^{-3j}=$$ rewrite $$S_j=\sum_{j=1}^{\infty} 27^{j-1}$$ using the geometric formula $$\sum_{n=1}^{\infty}ar^{n-1}=\frac{a}{1-r}, \left| r \right|<1$$ how do we get $a$ and $r$ to get the answer of $\frac{1}{26}$ ☕

Homework Statement I am asked to draw the ray diagram for an incident plane wave whose rays are at an angle α with respect to the optical axis of the telescope. I have done this, but I need to find an expression for the angle between the outgoing rays and the optical axis, in terms of f1, f2...

I would like to prove Feynman's denominator formula: ##\frac{1}{A_{1}\dots A_{n}} = (n-1)!\int_{0}^{1}dx_{1}\dots dx_{n}\delta(x_{1}+\dots+x_{n}-1)(x_{1}A_{1}+\dots+x_{n}A_{n})^{-n}## I was wondering if you would recommend brute force approach to solving this problem. I proved the formula for...

In a isobaric process W=PΔV I Given the change in temperature and pressure is constant to find heat added to an mono-atomic ideal gas we use Q=ΔU + W = 3/2 nRΔT + PΔV = 3/2 nRΔT + nRΔT so Q=5/2 nRΔT correct? II But given the heat added to an ideal gas, constant pressure that acts on the...

Is it the typical "get some results and stack the maths together and chuck in some constants to make it fit to get some approximation" or do we understand the rules behind it to derive the formula, such as how the molecules repel each other and how energy is transferred depending on temperature...

I have developed a script in MATLAB that can detect peaks from datas and that can find FWHM of detected peaks. Scripts gives reliable results but crystallites sizes are different a little from this http://mahendrakoppolu.blogspot.com.tr/2013/07/online-crystallite-size-calculator.html Link to my...

Homework Statement When the distance to a sound source is doubled, the noise level will be halved. Yes or no? Homework Equations L = 10 lg(I/10-12) or L = 10 lg(I/l0) The Attempt at a Solution my book used the first formula in another question and it used the second one in this problem. I...