Transformation Definition and 1000 Threads

I have to find a unitary transformation that takes me from one quantum state to another (or if there is such a transformation), given the two quantum states in matrix form. The matrices are huge (smallest is 16x16) , so doing it on paper is not an option. Does anyone know how I can do this in...

Homework Statement Show that if a transformation ##\Phi \rightarrow \Phi + \alpha \partial \Phi/ \partial \alpha## is not a symmetry of the Lagrangian, then the Noether current is no longer conserved, but rather ##\partial_{\mu}J^{\mu} = \partial L/ \partial \alpha##. Use this result to show...

I will start with a summary of my confusion: I came across seemingly contradictory transformation rules for left and right chiral spinor in 2 books, and am unable to understand what part is Physics and what part is convention. Or is it that one of the two books incorrectly writes the...

1. Problem statement: Assume that u is a vector and A is a 2nd-order tensor. Derive a transformation rule for a 3rd order tensor Zijk such that the relation ui = ZijkAjk remains valid after a coordinate rotation.Homework Equations : [/B] Transformation rule for 3rd order tensors: Z'ijk =...

So I am going through the exam guide for my exam tomorrow and there is a second problem that stump me. We transform the cartesian axis to <1/√3,1/√3,1√3> and <1/√2,0,-1/√2> which are orthogonal and we find the third axis by taking the cross product which gives <-881/2158,881/1079,-881/2158>...

Hi, I have a reference device that outputs euler angles, which are angles that relate the sensor body frame to the north east down frame. These angles are called pitch roll and yaw. The sensor is an accelerometer. I know how to get the rotation matrix that will put accelerations from the...

I'd like to prove the fact that - since a rotation of axes is a length-preserving transformation, the rotation matrix must be orthogonal. By the way, the converse of the statement is true also. Meaning, if a transformation is orthogonal, it must be length preserving, and I have been able to...

Homework Statement Homework EquationsThe Attempt at a Solution I would just like to know what is being requested when it asks me to draw sketches in order to illustrate that T is linear. Does it have something to do with altering to position of the line L itself? Any help would be very much...

My maths teacher taught me a shortcut for finding area bounded by curves of the form: $$|as+by+c|+|Ax+By+C|=d$$ Shortcut: Let required area be ##A_0## and new area after "transformation" be ##A## Then, $$A_0\begin{vmatrix} a& b\\ A& B\end{vmatrix}=A=2d^2$$ All I understood was the ##A=2d^2##...

1,2,3. Homework Statement I tried to derive the length contraction using the Lorentz transformation matrix and considering 2 events. I reached the correct result but there's a step that I had to assume that I don't understand. Consider a ruler of length L along the x-axis for an observer at...

Homework Statement Being T: ℝ2 → ℝ2 the linear operator which matrix in relation to basis B = {(-1, 1), (0, 1)} IS: [T]b = \begin{bmatrix} 1 & 0\\ -3 & 1 \end{bmatrix} True or False: T(x,y) = (x, 3x+y) for all x,y∈ℝ? Homework EquationsThe Attempt at a Solution 3 [/B] So first I convert (x,y)...

Hello everyone, I have a little problem with some transformation. I wonder how i can get that result. Can somebody explain it step by step? The " ' " means derivative. Thank you for your time ;)

Homework Statement Let A and B be n x m matrices, and λ and μ be real numbers. Prove that: (λA+μB)^T = λA^T+μB^t Homework Equations :/ The Attempt at a Solution I'm struggling to start here. If there was no λ and μ, I think I'd be able to reasonably solve this. How do I show that these...

Consider a model with an exact ##SU(N_{TC})## techni-color symmetry and a ##SU(N_{TF})_L\otimes SU(N_{TF})_R## global techni-flavour symmetry which is spontaneously broken to the diagonal sub-group ##SU(N_{TF})## by condensates producing techni-pions (TC\pi) and techni-baryons(TCb). What I'm...

Hello, I am stuck on the following problem. 1. Homework Statement Consider the continuous family of coordinate and time transformations (for small ##\epsilon##). Q^{\alpha}=q^{\alpha}+\epsilon f^{\alpha}(q,t) T= t+\epsilon \tau (q,t) Show that if this transformation preserves the action...

Here is a problem: Imagine two equally charged capacitor plates parallel to the x-y axis, whose area is large enough compared to the distance between them that fringe effects can be ignored. The bottom plate (at z=0) is + charged, and the top is - charged. The vector field E is therefore...

Given the Lorentz matrix Λuv its transpose is Λvu but what is its transpose ? I have seen ΛuaΛub = δb a which implies an inverse. This seems to be some sort of swapping rows and columns but to get the inverse you also need to replace v with -v ? Also In the LT matrix is it the 1st slot...

Homework Statement Suppose a linear transformation T: [P][/2]→[R][/3] is defined by T(1+x)= (1,3,1), T(1-x)= (-1,1,1) and T(1-[x][/2])=(-1,2,0) a) use the given values of T and linearity properties to find T(1), T(x) and T([x][/2]) b) Find the matrix representation of T (relative to standard...

Lets suppose we have a close system.In this system we have a particles.The total mass of particles is M. The total energy of system will be ##E_x+E_M=E_t## (I made the system like this) Here ##E_x## is just energy,its not important.##E_m## is the energy of masses.Now I want to move this...

<< Thread moved to the HH forums from the technical engineering forums, so no HH Template is shown >>[/color] The model: The goal: 1. Create a three phase voltage 2. Do a alpha-beta transformation 3. Do a Cartesian to Polar transformation 4 Check the output angle The expected result: Since...

We were asked to form the transformation matrix that rotates the x1 axis of a rectangular coordinate system 60 degrees toward x2 and the x3 axis. The thing is, I don't understand what it meant by rotating one axis toward the two other. Like, do I rotate x1 60 degrees toward the x2-x3 plane or...

Homework Statement Let T:[R[/3]→[R[/3] so that when u=[R][/3] and v=(1,2,1), then T(u)=u×v a) Show that T is a linear transformation. b) Find T((3,0,2)) c) Find a basis for Ker( T ). Give a geometric description of Ker( T ). Homework Equations Properties of a linear transformation: i) T(u+v)=...

I can't understand the transformation can anyone explain it to me.and suggest a good book on it.

Homework Statement Transform the coordinates from the red c-system to the blue system. (Picture) Homework Equations Using(X Y) for the red cartesian system and (x y) for the blue system The Attempt at a Solution The solution to this problem gives x=Xcos▼ + Ysin▼ y=-Xsin▼+Ycos▼ Im not sure...

I am confused about the order in which we apply transformations to a input of a parent function to get the corresponding input of the new function. Say for example, we have the function ##y = \sin(-2x + 1)=\sin(-2(x-\frac{1}{2}))##. Intuitively, it would seem as though we would transform a point...

Homework Statement Let T:V→V be a linear operator on a vector space V over C: (a) Give an example of an operator T:C^2→C^2 such that R(T)∩N(T)={0} but T is not a projection (b) Find a formula for a linear operator T:C^3→C^3 over C such that T is a projection with R(T)=span{(1,1,1)} and...

I want to try this bilinear transformation of a rectangle to a quad described here http://www.fmwconcepts.com/imagemagick/bilinearwarp/FourCornerImageWarp2.pdf on page 4. I have the square $$(500,900)(599,900)(599,999)(500,999)$$ and the quad $$(454,945)(558,951)(598,999)(499,999)$$ It...

Hello, I'm reading Tong's lecture notes on QFT and I'm stuck on the following problem, found on p.11-12. A scalar field \phi , under a Lorentz transformation, x \to \Lambda x , transforms as \phi(x) \to \phi'(x) = \phi(\Lambda^{-1} x) and the derivative of the scalar field transforms...

Homework Statement Find the bilinear transformation that maps the points z1=infinity, z2=i, z3=0 to the points w1=0, w2=i, w3=infinity. Homework Equations w=(az+b)/(cz+d) The answer is -1/z The Attempt at a Solution We have: infinity --> 0 i --> i 0 --> infinity Since 0 goes to infinity...

When one considers a Lorentz transformation between two frames ##S## and ##S'##, such that the coordinates in ##S## are given by ##x^{\mu}## and the coordinates in ##S'## are given by ##x'^{\mu}##, with the two related by x'^{\mu}=\Lambda^{\mu}_{\;\;\nu}x^{\nu} then a scalar field ##\phi (x)##...

Homework Statement [/B] Find a 2 x 2 matrix that maps e1 to –e2 and e2 to e1+3e2Homework Equations [/B] See the above notesThe Attempt at a Solution [/B] I am making a pig's ear out of this one. I think I can get e1 to –e2 3 -1 1 -3 but as far as getting it to reconcile a matrix like...

Hello, a derivation of the lorentz transformation for an arbitrary direction of the relative velocity often makes use of writing the spatial position vector of an event as the sum of its component parallel and perpendicular to the velocity vector in one inertial frame and then transforming both...

Hi, I'm writting a program in the computer and I've to perform a fast Fourier transform to get the frequency domain information. I've read different website, I've watched some videos, etc and I don't fully understand the whole theory about FFT. I've to say that I don't have a solid mathematics...

When proofing the poisson brackets algebraically, what is the tool of choice. Can one use the muti dimensionale chain rule or how is it usally done?

Homework Statement What is the maximum mass of lead you could melt with 2000 J of heat, starting from 25 ∘C ? Lead melts at 328∘C , its specific heat is 128 J/(kg⋅K) , and its heat of fusion is 2.5×10^4 J/kg . Homework Equations Need to find both the mass in the heat of transformation (Q =...

Warning...this requires scripting and iteration, and is not theoretical -- it is a real problem I haven't been able to solve, but I'm sure someone here can... :-) Data: each .csv file is a test recorded at a time interval of 7.5Hz and each file has 3 columns. The first column is time in...

This is problem 11.15 of Jackson, Classical Electrodynamics In a certain reference frame a static, uniform, electric field Eo is parallel to the x axis, and a static, uniform, magnetic induction Bo = 2Eo lies in the xy plane, making an angle theta with the axis. Determine the relative velocity...

Homework Statement Consider ##\mathscr{H} = \frac12 p^2 + \frac12 x^2, ## which is invariant under infinitesimal rotations in phase space ( the ##x-p## plane). Find the generator of this transformation (after verifying that it is canonical). Homework EquationsThe Attempt at a Solution So the...

Homework Statement So we have infinitesimal transformations from ##q_i## to ##\bar{q_i}## and ##p_i## to ##\bar{p_i}## ( where ##p_i## represents the canonical momentum conjugate of ##q_i##) given by $$\bar{q_i} = q_i + \epsilon \frac{\partial g}{\partial p_i}$$ $$\bar{p_i} = p_i - \epsilon...

I'm extreeeeamly rusty at basic circuit theory. I want to transform a sort of infinite arrangement of this circuit: The values themselves aren't important, just the representation of what's happening, all the verticle resistors are the same value as each other, and all the horizontal resistors...

Hello, I'm running a galaxy formation simulation. The output specifies the coordinates in (x, y, z) of all the particles in a galaxy, which usually fall in a disk. The orientation of the disk depends on the initial conditions, but it is generally not aligned with any of the coordinate axes...

Hey everyone! It's my first semester with quantum mechanics and I'm uncertain if my solution of this problem is correct, would be nice if someone could check and let me know :smile: 1. Homework Statement I have to calculate the representation of the state: |\alpha \rangle \equiv exp[-i...

I would like to obtain the conformal map from a uniform rectilinear fluid flowing in the x-direction, where the field is bounded below by the x-axis, to the flow in the w-plane. In the w-plane the flow is correspondingly bounded from below by a trochoid. (A trochoid is a continuous waveform...

Dear PF Forum, First, I'd like to thanks this forum for helping this much and so far. I have a question about Lorentz Transformation. Lots of questions actually :smile: http://en.wikipedia.org/wiki/Lorentz_transformation#Boost_in_the_x-direction Instead of using t and x, I'd like to use ta and...

Homework Statement Find the two numerical values of λ such that \left(\begin{array}{cc}4&3\\1&2\end{array}\right) \left(\begin{array}{cc}u\\1\end{array}\right) =λ \left(\begin{array}{cc}u\\1\end{array}\right) Hence or otherwise find the equations of the two lines through the origin which...

Homework Statement Light (plane wave) reflects from the mirror moving along X-axis with speed V. The wave is orthogonal to the mirror (φ=0°). Write the law for frequency change. Homework Equations I know Lorenz transformation for frequency. The Attempt at a Solution All I do not know is how to...

Homework Statement Describe the transformation in : y=e6x-2 - 4 y=6ex-2 - 4 ? Homework Equations --- The Attempt at a Solution 1)So 6x means stretch parallel to x-axis at s.f of 1/6 and then translation of ( +2 , -4 ) 2) the same but the stretch is parallel to y-axis at s.f of 6 but...

Hello, I have some mathematics background but little to no physics background. I am very interested in physics and am beginning to learn about relativity. Upon exploring the derivation of the Lorentz Transformation equation I noticed something that confused me a little. Again, I don't have much...

1- Let the linear operator on R^2 have the following matrix:A = 1 0 -1 3 What is the area of the figure that results from applying this transformation to the unit square? 2- I am abit confused here, I thought that the matrix for the unit square would be, 0 0 1 0 0 1 1 1... But...

hi guys :D im having trouble with this proof, any hints? let V be a vector space over a field F and let T1, T2: V--->V be linear transformations prove that