deriving Definition and 962 Threads

In A. Zee "QFT in a nutshell" in chapter I.5 on page 31 how does equation (3) come about? Just the line above this equation, he gives an equation which needs to be rearranged to give (3). It must be embarrassing simply, but I can't see how. Something with the indices goes on. How does the...

Say you have the coefficients a_k of a Fourier series representation of some function x(t). You can easily then give x(t) as $$x(t) = \sum_{k = -\infty}^{\infty} a_k e^{i k \omega_0 t}$$ But this doesn't do much good in telling you what the actual function looks like. For example, if we have...

Homework Statement Derive the following general relation : \left(\frac{\partial T}{\partial V}\right)_{S} = - \frac{1}{C_{V}} T \left(\frac{\partial p}{\partial T}\right)_{V} Homework Equations Maxwell's Relation : \left(\frac{\partial T}{\partial V}\right)_{S} = - \left(\frac{\partial...

I'm trying to derive/simplify Fresnel's equation for r perp from its form: [ni cos \thetai - nt cos\theta t] / [ni cos \theta i + ntcos\thetat] to ---> - sin (\thetai - \thetat) / sin (\thetai + \thetat) From what I've gathered you need to use Snell's law ntsin\thetat = nisin\thetai and...

Homework Statement Suppose there is a Conical section (of a right circular cone) of total height 'l' and radii 'a' and 'b' (a>b). How do we derive the formula for the radius at a height 'h' (h<l) ?Homework Equations The Attempt at a Solution

Hi, I'm having a bit of trouble in my second semester of physics. We're covering magnetism right now. I can understand a derivation put before me of, for example, the torque due a current passing through a wire loop. However, I could never recreate this or reach a similar conclusion on my own. I...

Homework Statement A circular curve of radius R in a new highway is designed so that a car traveling at speed v0 can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will slip...

Deriving Vr and V(sub-theta) from Kepler's second law and... Homework Statement Beginning with r=[a(1-e2)]/(1+e*cos \theta) and Kepler's second law, derive general expressions for vr and v\theta for a mass m1 in an elliptical orbit about a second mass m2. The final answers should be...

I'm studying optics on my own and have gotten very stuck on page 75 of Klein and Furtak, the unnumbered equation. Specifically, I don't understand why there aren't arbitrary phase factors inserted; the equation does not look general enough. I checked in Jackson, 2nd edition Classical...

Homework Statement The velocity of a proton relative to our galaxy is vp/c = 1-(0.5*10^20), i.e. almost one. Such protons are actually observed. When velocity it very nearly one \gamma is very large. 1/\gamma is very small. Use Taylor series to show that for v almost one we have...

Homework Statement Hi again folks! I just need confirmation on this, since I'm quite sure I've got it right. Anyway here it goes. The position of a particle is given by the function x(t)= A + Bt + Ct² + Dt³. The values of the constants are the following: A= 4,0; B=2,0; C= -3 and D=1,0. a)...

Homework Statement A particle moves along the y-axis according to y(t)=(3.5 m/s2)t2 - (9.0 m/s)t + 5.0 m. (a) What is the particle's velocity as a function of time? (b) What is the particle's acceleration at t=2.0 s? The Attempt at a Solution I was wondering about b- I derived: dy/dt...

Homework Statement An asteroid moves toward the sun along a straight line with a velocity given by v = -(c1+c2/x)½ , where x is the distance from the center of the sun. Use the chain rule for derivatives to show that the asteroid's acceleration is a = -c2 /2x2. The Attempt at a Solution...

E=mc^2 and E=hf. In Special Relativity, how can y=h/p be derived from E=hf?

How can the tan power series be derived from the sin and cos power series? Where do the Bernoulli numbers come in?

I'll first derive here the gravitational pot. energy by my method, and then I'll give the method that has been formally used in books. My answer differs from the actual one by a minus sign. My derivation: Let mass M be at the origin O. Let another mass m be at an arbitrary position r from...

Everyone knows by now that a conic section is the figure formed when a plane intersects a right circular cone. Most everyone also knows that there are many different ways to describe a conic, geometrically and algebraically. What one seldom sees is the derivation of those descriptions from the...

I know what the definition of torque and angular momentum is. But I read in a few books that "Torque and angular momentum are not independent laws of nature, and have been derived from the more fundamental laws of Newton." The above simply means, that the rotational motion is just a...

Hi! This is my first post, so i apologise if i leave out any information. I need to derive an expression for the theoretical velocity of flow in an open channel using the Bernoulli Equation. I realize it is probably a simple question but i am sort of a beginner. Any help appreciated...

I am writing a system that collects values from our devices (CRAH, Generators, etc) compute the trend of the data, and determine if an alarm should be raised. For testing I have a point generator and I want it to follow fairly realistic norms. Currently I generate a new point as: p.Y = p'.Y...

Homework Statement The mean free path for an ideal collisional gas can be calculated as shown on thishttp://hyperphysics.phy-astr.gsu.edu/hbase/Kinetic/menfre.html" . I understand the derivation, except for one thing. Homework Equations The Attempt at a Solution The molecule is...

I am trying to follow along with this derivation of the binomial distribution formula: b(x;n,p) = nCx*pxqn-x But I do not really understand the meaning of the part on bold. What is this "specified order" business now? I feel like I am missing something big here.

I am working with the Keplerian Elements from the JPL web site. a - Semi-Major Axis e - Eccentricity I - Incilination L - Mean Longitude long.peri. - Longitude of the Periapsis long.node.or N - Longitude of the Ascending Node http://ssd.jpl.nasa.gov/txt/p_elem_t2.txt From this...

Hello, it is mentioned http://en.wikipedia.org/wiki/Atan2#Definition" that using the tangent half-angle formulas it is possible to express the function atan2 as: \mathrm{atan2}(y,x)=2\mathrm{arctan}\frac{y}{\sqrt{x^2+y^2}+x} How can I derive this result?

Can anyone help me with this? My textbook (Young and Freedman's University Physics) says that Ampere's law can be extrapolated to give Biot Savart's law but I'm not sure how to go about it.

Homework Statement if y=logε((1 + √x)(/1- √x )) , show than dy/dx = (1/(√x(1-x)) The Attempt at a Solution y=logε((1 + √x)(/1- √x )) y=logε(1+√x)-logε(1-√x) dy/dx = 1-1/(1+√x) + 1/(1-√x) i don't no what to do after this or if I am even going in the right direction!?

Homework Statement The Pitt Fall is thrill ride at Kennywood that lifts passengers to a certain height, pauses for a few moments, and then drops the riders, causing them to free fall towards the ground before gradually applying breaks 79 ft above the ground. Assume there is a drag force, F=-bv...

Homework Statement Find the Laplace transform of each of the following functions: ... 2. f(t)=eatcos(bt) 3. f(t)=tn, were n is a positive integer Homework Equations As you well know, taking the Laplace of f(t) means ∫f(t)e-stdt from 0 to ∞ The Attempt at a Solution...

Hi, I was wondering if someone could show me how this was derived from dv/dt? I was trying to look in my notes but I think I may have copied something down wrong. This isn't a homework question but I just like to know how it works. Thank you. d(1/2v2)/dx

Homework Statement Derive from Newton II the thrust (the force produced by the rocket exhaust) achieved by a rocket motor which ejects material with constant velocity u and mass ejection rate a. Homework Equations The Attempt at a Solution Not sure...I know how to derive vf =...

Homework Statement I did the question with help, but did not understand why did we multiply e^-i(x/2) How do I know what to multiply for getting the real part of a complex number in exponential form? Homework Equations The Attempt at a Solution

I looked at my notes, but they're either incomplete or I simply forgot what the professor did to derive the gradient in spherical coordinates. Once I know that, deriving the divergence and curl given the supplementary equations listed is fairly straightforward. It was a little easier but...

Homework Statement Derive the Gauss Variational differential equation for the true anomaly, f, with respect to time using components along the radius, angular velocity, and a unit vector orthogonal to those two (ir,itheta,ih). Homework Equations Sorry, I don't know how to use Latex. But...

Given Kepler's Laws how do you derive Newton's Law of Gravitation?

I look for derivation of Ernst equation - an equation for complex function which is equivalent to Einstein equation in case of metric with two commuting killing vectors. I know this equation but I wonder how it may be derived. I also heard that teher is a simple procedure which allow to...

Homework Statement Given: f(x,y) = x + y, for 0<x<1 and 0<y<1 f(x,y) = 0, otherwise Derive the joint distribution function of X and Y. Homework Equations N.A. The Attempt at a Solution Using the definition, I obtained part of the joint distribution F(x,y) = (1/2)(xy)(x+y)...

Homework Statement Derive a formula of the form \int\stackrel{b}{a}f(x)dx \approx c_{0}f(a)+c_{1}f(b)+c_{2}f'(a)+c_{3}f'(b) that is exact for polynomials of the highest degree possible. Apply a change of variable: y=x-a Homework Equations The Attempt at a Solution I don't get the "highest...

I've read a few papers about derivation of the Schwarzschild metric by using the equivalence principle ( http://cdsweb.cern.ch/record/1000100/files/0611104.pdf" )... but I couldn't understand them completely they assume , According to Einstein’s equivalence principle, that the influence of...

Homework Statement Hi. For a project I have to derive this formula for bright fringes in optics, but I'm stuck on this simple math part (or maybe its not so simple)...ive attached a picture of where i don't understand...it might be considered a simple math problem so I'm sorry if this is too...

I have seen the derivation for the formula: h2(pi)rdr used in math textbooks. However, earlier today I had a physics problem where I needed to use the volume of a cylindrical shell of inner radius r and outer radius dr+r and length h. without remembering the formula I tried to derive it...

Homework Statement Find the centroid of the region cut from the first quadrant by the circle x^2+y^2=a^2Homework Equations I know that y' = (I y dA)/(I dA)The Attempt at a Solution Taking a strip dy with length x, I obtain dA = dy.x dy(a^2-y^2)^(1/2) So I y DA = I y*(a^2-y^2)^(1/2) dy from...

In class we have been deriving the Fraunhofer interference pattern for a double slit experiment. I now have a question of having to derive it if one of the slits is covered with an absorbing material. I have got the equation out but I am missing a constant K... Homework Statement We have two...

Homework Statement Take the Schrodinger equation for a point particle in a field: i\hbar \frac{\partial \Psi}{\partial t} = \frac{1}{2m}(-i\hbar\nabla - q\vec{A})^2\Psi + q\phi\Psi I'm supposed to determine what the transformation for Psi is that corresponds to the gauge transformation...

Consider a heat equation for the temperature u of a rod of length 1: ut = uxx, 0 < x < 1, t > 0 with boundary conditions ux(0,t) = 0 & u(1,t) = 0. I derived Xn(x) = cos((n+1/2)\pix) using separation of variables. How do I show that \int_{0}^1 Xn(x)Xm(x) dx = 1/2 if m = n and 0 if m...

exp[m1t-m2t-m3t] mew-number bottom right-t Since t is common to each, there must be a better way of writing that. I am using equation editor with word, which doesn't paste here. Any help gratefully received.

Hi everyone, I'm trying to understand the derivation of D(x,t) = A \sin{(kx - \omega t + \phi_o)} which is the displacement equation for a sinusoidal wave. The way my textbook (Physics for scientists and engineers by Knight) does it: Look at the graph of displacement versus position at time...

Okay, we all know that ΔX = ViT + 1/2AT^2 Say I drop a stone from rest and I want to find its distance at a given time knowing the acceleration. Since the initial velocity is zero and its accelerating vertically we can say. ΔY = 1/2AT^2 ΔY = (AT^2) / 2 <------------------------- Keep in mind...

where x represents cross product currently if i forget i figure these out using the right hand rule, but how do you get each equation visa versa using vector algebra i started with w = rxv how do you derive that v = wxr i got up to this w = rxv w= -(vxr) rxw = -rx(vxr) rxw =...

Hello; How is this formula derived? And why is the speed of light squared? Is there a reason for that? Thanks.

Homework Statement I'm supposed to derive the following: \left({\bf A} \cdot {\bf \sigma} \right) \left({\bf B }\cdot {\bf \sigma} \right) = {\bf A} \cdot {\bf B} I + i \left( {\bf A } \times {\bf B} \right) \cdot {\bf \sigma} using just the two following facts: Any 2x2 matrix can...