Transformation Definition and 1000 Threads

I understand ##\vec A\rightarrow\vec A+\nabla \psi\;## as ##\;\nabla \times \nabla \psi=0##\Rightarrow\;\nabla\times(\vec A+\nabla \psi)=\nabla\times\vec A But what is the reason for V\;\rightarrow\;V+\frac{\partial \psi}{\partial t} What is the condition of ##\psi## so \nabla...

Hello everyone, I've been thinking about energy transformations and an electrical generator came to my mind which basically transforms mechanical energy into electrical energy. What confused me as I was thinking about it is whether the electrical energy that results due to the rotation of the...

Ok, this should be an easy one but it's driving me nuts. When we take the Lorentz transformations and apply them to x2-c2t2 we get the exact same expression in another frame. I can do this math easily by letting c=1 and have seen others do it by letting c=1 but I have never seen anyone actually...

Can one explain the relativistic energy transformation formula: E = \gamma\ E', where the primed frame has a velocity v relative to the unprimed frame, in terms of relativistic time dilation and the quantum relation E=h\ f? I imagine a pair of observers, A and B, initially at rest, each...

Homework Statement Hi all. I am having trouble to understand the combination of transformation on a function: h(x)= a*f(b(x-c))+dHomework Equations The problem I am struggling with is the order of transformation; I do see that: f(x-c) is translation in the right since every event happen before...

Homework Statement The problem is tough to type out correctly. Pasting problem statement image http://postimg.org/image/a0r92a0wl/ http://postimg.org/image/a0r92a0wl/ The Attempt at a Solution I just need to know how to proceed with the problem. Not the answer. This is the scan...

There is something I'm struggling with and I can't seem to find the problem. We have the Z spinbase with: z = (1/sqrt(2))² <BRA|*(|s_z,+> + |s_z,->) which gives following z matrix: 1 0 0 1 and we have for X: |s_x, +> = 1/sqrt(2) |s_z,+> + |s_z,->) |s_x, -> = 1/sqrt(2)...

Homework Statement Find surface inside four boundary curves: xy = 4 , xy=8 , y=5x , y=15x using the transformation: u=xy , v=\frac{y}{x} Homework Equations I'm getting the new bounds to be: 4 < u < 8 , -15 < v < -5 OR 5 < v < 15 Jacobian is \frac{1}{2v}The Attempt at a...

I'm doing a research project currently and basically what I have is a camera measuring a probe. I have designed the camera to give the orientation of the probe using euler angles in the camera's frame of reference. This was working for most of my data, but now I need a 3-D visualization of what...

Hi to all! I have the following transformation \tau \to \tau' = f(\tau) = t - \xi(\tau). Also I have the action S = \frac{1}{2} \int d\tau ( e^{-1} \dot{X}^2 - m^2e) where e = e(\tau) . Then in the BBS String book it says that $$ {X^{\mu}}' ({\tau}') = X^{\mu}(\tau)$$ and...

This is probably a stupid mistake I am making, but I can't figure it out. My apologies in advance... I am familiar with the text-book derivation of the Lorentz transformation (I don't have any problem with it). It starts out stating: x2+y2+z2-c2t2 = x'2 + y'2+z'2-c2t'2 meaning that a...

I want to transform from rectangular coordinates ( xyz) to (x",y",z") rectangular coordinates that is rotated at the origin as show in the attachment. Then I want to transform (x",y",z") rectangular coordinates into Spherical coordinates. Attach is the method I use, I want to verify I am doing...

I have sets of 2d vectors to be transformed by an augmented matrix A that performs an affine transform. Matrix A can have values that differ at most |d| from the identity matrix, to limit the transformation, meaning that the min/max bounds for A are I_3 \pm dI_3 The problem is that i'd lke...

Given a specific metric, is there a easy way to transform it in Synchronous coordinates? For example having dsigma2 = (1+z)^2 dt^2 - ds^2 - s^2 dphi^2 - dz^2 , I was able to do some substitutions, but I had to stop at the differential equations presented in the attachement.

For a certain transformation T, it is known that T(x+y) = T(x) + T(y) It is required to determine whether this transformation is linear. Obviously it is not, since it need not satisfy the degree-1 homogeneity property of all linear maps. I'm just having trouble cooking up the...

Resource: Linear Algebra (4th Edition) -David C. Lay I understand that there are identities associated with transformations, but what I don't understand is when the transformation is rotated about the origin through an angle β. I believe β in this case is \frac{}{}\pi/2 \left[1,0\right]...

Homework Statement Hello Guys, I am reading Hobson's General Relativity and I have come across an exercise problem, part of which frustrates me: 3.20 (P. 91) In the 2-space with line element ds^2=\frac{dr^{2}+r^{2}d\theta^{2}}{r^{2}-a^{2}}-\frac{r^{2}dr^{2}}{{(r^{2}-a^{2})}^{2}} and...

If X is a random variable distributed uniformly in [0, Y], where Y is geometric with mean alpha. i) Is this definition valid for uniform distribution ? ii) If it is valid, what is the pdf of the transformation Y-X?

Hello MHB, given a linear transformation F so that this is known \left\{ \begin{aligned} \phantom{1}F(1,0,0)=(1,2,3) \\ F(1,1,0)=(0,0,1)\\ F(1,1,1)=(12,3,4)\\ \end{aligned} \right. Decide F progress: F(e_1)=(1,2,3) F(e_2)=F(e_1)+F(e_2)-F(e_1)=(0,0,1)-(1,2,3)=(-1,-2,-2)...

Homework Statement I am a bit confused on why they can just randomly short the 4kΩ resistor, as you can see from the first pic to the second pic. THanks Homework Equations The Attempt at a Solution

Homework Statement Use source transformation to find the Thevenin equivalent circuit with respect to terminals, a, b. Homework Equations Voltage Division: (V in)*(R1/R1+R2) Thevenin / Norton / source transformation procedures RTh = RNo VTh = INo*RNo Polar...

The Schwarz-Christoffel mapping (a Riemann-mapping) from the unit disk (z-plane) to a twice-symmtric area (a cross, ζ-plane) $$ \zeta : \mathbf C \to \mathbf C $$ is given by: $$\frac{ \mathrm{d}\zeta }{ \mathrm{d} z} = \left( \frac{ ( z^2-b^2 ) ( z^2-\frac 1 {b^2} ) }{ ( z^2-a^2 ) (...

In a recent course on special relativity the lecturer derives the Lorentz transformation matrix for the four vector of position and time. Then, apparently without proof, the same matrix is used to transform the EM field tensor to the tensor for the new inertial frame. I am unclear whether it...

Hi Everyone, I was studying coordinate transformation and I came across this equation, that I couldn't understand how it came up. Let me put it this way: x = rcosθ Then if I want to express the partial derivative (of any thing) with respect to x, what would be the expression? i.e. ∂/∂x=...

Homework Statement Use source transformation on the voltage source and series-connected impedance for the circuit shown here to find the equivalent current source and parallel-connected impedance. Continue the simplification by combining the two parallel current sources into an equivalent...

I am trying to learn how to use phase transformation diagrams and I don't get it. Any help from someone who knows about this would be greatly appreciated (I have a final tuesday) An example problem is below with the picture attached. I have to be able to find what the microstructure is after...

Where T(p(x)) = (x+1)p'(x) - p(x) and p'(x) is derivative of p(x). a) Find the matrix of T with respect to the standard basis B={1,x,x^2} for P2. T(1) = (x+1) * 0 - 1 = -1 = -1 + 0x + 0x^2 T(x) = (x+1) * 1 - x = 1 = 1 + 0x + 0x^2 T(x^2) = (x+1) * 2x - x^2 = 2x + x^2 = 0 + 2x + x^2 So, the...

How do we go about finding the transformation that was used to go from one matrix to another ( provided of course that the two are linked by a transformation) in general if all we have is two matrices.

Hi. I'm reading about non-abelian theories and have thus far an understanding that a gauge invariant Lagrangian is something to strive for. I previously thought that the Yang-Mills gauge boson free field term ##-1/4 F^2 ## was gauge invariant, but now after realizing that the field strength...

Hi, I'm having trouble understanding the purpose of using two basis in a linear transformation. My lecturer explained that it was a way to find a linear transformation that satisfied either dimension, but I'm having trouble understanding how that relates to the method in finding this...

Hi All, I have a question about transformation matrices (sorry about the typo in the title). The background is that I've spent some time learning differential geometry in the context of continuum mechanics and general relativity, but I'm unable to connect some of the concepts. So I have this...

Dirac Equation as Example, Dirac Equation: \left(i\gamma^\mu \partial_\mu -m \right)\psi(x)=0 Can I write it in the following way? \left(i\gamma^0 \partial_0- i\gamma^j \partial_j -m \right)\psi^p(t,{\bf -x})=0

Problem: Suppose that $X \text{ ~ Exp}(\lambda)$ and denote its distribution function by $F$. What is the distribution of $Y=F(X)$? My attempt: First off, I'm assuming this is asking for the CDF of $Y$. Sometimes it's not clear what terminology refers to the PDF or the CDF for me. $P[Y \le y]=...

This is something that when I see the work done it makes sense, but I find it difficult to do myself. I'm also aware there is an explicit formula for doing this but that involves Jacobians and a well-defined inverse, so I think it's more intuitive to do it step-by-step. Problem: Suppose $X...

Homework Statement My quantum mechanics text (in an appendix on linear algebra) states, "f the eigenvectors span the space... we are free to use them as a basis..." and then states: T|f1> = λ1f1 . . . T|fn> = λnfn My question is: is it not true that fewer than n vectors might...

Help please. I can't find what am I missing. The solution is in the attachment. Thanks in advance.

I've had to hit my books to help someone else. Ugh. Say we have the coordinate transformation \bf{x}' = \bf{x} + \epsilon \bf{q}, where \epsilon is constant. (And small if you like.) Then obviously d \bf{x}' = d \bf{x} + \epsilon d \bf{q}. How do we find \frac{d}{d \bf{x}'}? I'm missing...

I am starting to deal with optomechanical systems as part of my work, and am faced with what seems to be an uncomplicated problem, however I'm ashamed to admit that I am having great difficulty getting to grips with it. I'd like some pointers and/or advice as to how to go about solving these...

Homework Statement Write down the 2 × 2 matrix that represents the following linear transformation of the plane. Also draw the image of the (first quadrant) unit square 1. T(x, y) = (2x +6y, x + 3y). Homework Equations T(x, y) = (2x +6y, x + 3y). The Attempt at a Solution So...

Homework Statement Show that the following linear transformation matrix is a contraction mapping. \begin{bmatrix} 0.5 & 0 & -1 \\ 0 & 0.5 & 1 \\ 0 & 0 & 1 \end{bmatrix} I don't know how to make that into a matrix, but it is a 3x3 matrix. The first row is [.5 0 -1] the second row is [0...

Homework Statement Define a Function T : P3 → ℝ3 by T(p) = [p(3), p'(1), 0∫1 p(x) dx ] Show that T is a linear transformation Homework Equations From the definition of a linear transformation: f(v1 + v2) = f(v1) + f(v2) and f(cv) = cf(v) The Attempt at a Solution This is how...

Homework Statement Suppose A is an m x n matrix. (a) Let v1 ,...,vn be a basis of ℝn, and Avi = wi ε ℝm, for i = 1,...,n. Prove that the vectors v1,...,vn, w1,...,wn, serve to uniquely specify A. (b) Write down a formula for A.Homework Equations Maybe B = T-1 A S The Attempt at a Solution I...

I was thinking when I take the Lorentz formula for a location γ.(x – v.t) as an observer in S and find the ratio compared with the location for an observer within the inertial system S’ it selves: 1/γ . Δx But I made a mistake and took 1/γ. x When I use the found ratio (for derivation...

Homework Statement L: R^3 -> R^2 L(x)=(0,0)^T What is the basis, and dim of the Range? Homework Equations Rank(A)-Nullity(A)=n The Attempt at a Solution So clearly L(x)= (0,0)^T. So the basis must be the empty space and dim is zero, right? Now, going of this same logic, Say...

I want to discuss this because I afraid that the answer is no. In SR we stuck with the transformations from Poincare Group because this transformations leave invariant the exact form of the Lorentz Metric tensor. Any other transformation will change the components of the Lorentz Metric Tensor...

IR and NIR spectroscopy usually employ Fourier transformation to separate the signal into individual wavelength, UV and Vis spectroscopy normally apply gratings for light dispersion (into individual wavelength). What is the cutoff wavelength, and why is so?

Can Lorentz Transformation be applied directly to a four velocity vector? I mean let v_{α} be a four velocity vector. Is there a form of Lorentz tfm matrix such that: v^{'}_{α} = \Lambda^{β}_{α}v_{β} ?

Homework Statement We were told that it is a simple algebraic substitution to derive the t' expression from the x and x' equations for a lorentz transformation. However, I keep reaching a dead end in the algebra. Homework Equations x=B(x'+vt') x'=B(x-vt) B=1/(Sqrt(1-(v/c)^2)) B^2 = c^2/(c^2...

Hi, When I do the following transformation: $$ X_1=x_1+x_2 \\ X_2=x_2 $$ It turns out that the Jacobian ##\partial (X_1,X_2)/\partial (x_1,x_2)## is 1. But we have: $$ dx_1dx_1+dx_1dx_2=d(x_1+x_2)dx_2=dX_1dX_2=|\partial (X_1,X_2)/\partial (x_1,x_2)|dx_1dx_2=dx_1dx_2 $$ So we...

I've just started reading Arfken's book on mathematical methods for physics, and one of the very first sections is really confusing me. He is discussing the rotation of coordinates, and defining a vector as an object whose components transform in the same way as the coordinates do under a...