Transformation Definition and 1000 Threads

I'm reading modern physics, Tipler 5th edition, pages 21 and 22, and I'm not understanding how the differentiation was done from the position to find the velocity. Equation for position: x'= y(x - vt) y is the gamma constant. Then in the first step to find the velocity, a derivative was done...

Homework Statement Q10.20 Using the isothermal transformation diagram for a 1.13 wt% C steel alloy (Figure 10.39), determine the final microstructure (in terms of just the microconstituents present) of a small specimen that has been subjected to the following time–temperature treatments. In...

Homework Statement Show that T:C[a,b] -> defined by T(f) = ∫(from a to b) f(x)dx is a linear transformation. Homework Equations Definition of a linear transformation: A linear transformation T from a vector space V into a vector space W is a rule that assigns to each vector x in V a unique...

Homework Statement Homework Equations None. The Attempt at a Solution I know that the standard matrix of a counterclockwise rotation by 45 degrees is: [cos 45 -sin 45] [sin 45 cos 45] =[sqrt(2)/2 -sqrt(2)/2] [sqrt(2)/2 sqrt(2)/2] But the problem says "followed by a projection onto the line...

Homework Statement I'm not asking how to do this question This is a work done by one of my students And the highlighted part it seems to be the correct answer that the teacher gave. I cannot make any sense out of these two questions Perhaps one of you might shed some light on to...

Hello! I want to know how does a parity transformation affect Bloch states! I always knew that parity takes the position vector to minus itself (in odd number of dimensions), but I have read that it also takes the Bloch wave vector to minus itself but I have not found a satisfactory proof of...

Homework Statement I have to costruct a 2x2 matrix so that : The Attempt at a Solution M =\begin{bmatrix} a & b\\ c &d \end{bmatrix} Using the first bond i got : c+2d = 2a+4b (1) using the second bond : d = -b (2) And then, as a nilpotent matrix has det = 0 and tr = 0, i got a+d-2=0 (3)...

Is it possible to understand intuitively (without using a formal proof ) why a reflection is a linear function ?

Lorentz transformation of electromagnetic field gives the relation ##E'=\gamma(E+v\times B)##. Lorentz force per unit charge is given as ##F=E+v\times B## without ##\gamma##. Don't we need coefficient ##\gamma## for F?

Consider a Lagrangian: \begin{equation} \mathcal{L} = \mathcal{L}(q_1\, \dots\, q_n, \dot{q}_1\, \dots\, \dot{q}_n,t) \end{equation} From this Lagrangian, we get a set of ##n## equations: \begin{equation} \frac{d}{dt}\frac{\partial \mathcal{L}}{\partial \dot{q}_i} - \frac{\partial...

Hello. Here is the formula that computes the sample skewness: Sk = [ (n / [(n-1)(n-2)] ] x [ ∑ (Xi - X)3 / s3 ] , where n is the number of elements in the sample, Xi is the specific i-th value of the sample, where i starts from 0 and ends at i=n, X is the arithmetic mean, s - standard...

Homework Statement Let's have a three-particle decay of equal mass ##m##; in the CM frame the three particles have equal energy ##E## and they form angles of ##\frac{2\pi}{3}## between each other. Which is the angle between two of the three particles in the rest frame of the other one. (The...

Could you please help me to understand what is the difference between notions of «transformation» and «automorphism» (maybe it is more correct to talk about «inner automorphism»), if any? It looks like those two terms are used interchangeably. By «transformation» I mean mapping from some set...

HI .I'm trying to prove that, for a linear transformation, it is worth that: f(a\bar{x}+b\bar{y})=af(\bar{x})+bf(\bar{y}) for every real numbers a and b. Until now, I have proved by myself that f(\bar{x}+\bar{y})=f(\bar{x})+f(\bar{y}). and , using this result i proved that: f(a\bar{v}) =...

Is the Lorentz transformation matrix Λμν a tensor of order two and does it transform like a tensor ?

Homework Statement I am to solve an ODE using the Fourier Transform, however I am quite inexperienced in using this method so I'd like some advice: Homework Equations a) The Fourier Transform b) The Inverse Fourier Transform The Attempt at a Solution I started by applying the Fourier...

I am confused about the field transformation under conformal transformation. Consider the scale transformation of field ##\phi## (not necessarily scalar) In CFT of Francesco et al, formula (2.121), the transformation is $$ \vec{x}\rightarrow \vec{x}'=\lambda x,\,\,\,\phi(\vec{x}) \rightarrow...

I read somewhere that, suppose a scalar field Σ transforms as doublet under both SU(2)L and SU(2)R, its general rotation is δΣ = iεaRTaΣ - iεaLΣTa. where εaR and εaL are infinitesimal parameters, and Ta are SU(2) generators. I don't quite understand this. First, why does the first term have...

<<moved from a technical forum, no template>> Need a Solution ASAP!

I am reading Hugo D. Junghenn's book: "A Course in Real Analysis" ... I am currently focused on Chapter 9: "Differentiation on \mathbb{R}^n" I need some help with the proof of Proposition 9.2.3 ... Proposition 9.2.3 and the preceding relevant Definition 9.2.2 read as follows...

I am reading Hugo D. Junghenn's book: "A Course in Real Analysis" ... I am currently focused on Chapter 9: "Differentiation on \mathbb{R}^n" I need some help with the proof of Proposition 9.2.3 ... Proposition 9.2.3 and the preceding relevant Definition 9.2.2 read as follows: In the above...

I am reading Hugo D. Junghenn's book: "A Course in Real Analysis" ... I am currently focused on Chapter 9: "Differentiation on ##\mathbb{R}^n##" I need some help with the proof of Proposition 9.2.3 ... Proposition 9.2.3 and the preceding relevant Definition 9.2.2 read as follows: In the...

I have been learning SR from various sources. Most of the time from Feyman's Lectures but that's not the only place. In II_26 he gives the transformation for the E-field of a moving charge in the x direction under a standard Lorentz configuration. In Eqn 26.11 he derives a formula for the Ex...

I am reading Hugo D. Junghenn's book: "A Course in Real Analysis" ... I am currently focused on Chapter 9: "Differentiation on \mathbb{R}^n" I need some help with the proof of Proposition 9.2.3 ... Proposition 9.2.3 and the preceding relevant Definition 9.2.2 read as follows...

I am reading Hugo D. Junghenn's book: "A Course in Real Analysis" ... I am currently focused on Chapter 9: "Differentiation on ##\mathbb{R}^n##" I need some help with the proof of Proposition 9.2.3 ... Proposition 9.2.3 and the preceding relevant Definition 9.2.2 read as follows: In the...

Homework Statement I've never encountered Jacobians before, and having read up on them a bit I find the wording of the last part of this question confusing: A set of coordinates ##x'_{\mu}## in frame B is obtained from the set ##x_{\mu}## in frame A, by boosting B w.r.t A with speed beta along...

I am working through "Lessons on Particle Physics." The link is https://arxiv.org/PS_cache/arxiv/pdf/0906/0906.1271v2.pdf. I am on page 21, equation (1.5.50), which is ##S(\Lambda)=1-\frac{i}{2}\omega_{\mu\nu}\Sigma^{\mu\nu}##. I would like some motivation for this equation. I wonder what the...

Homework Statement Derick is fleeing from the cops on a car on a relativistic train. At xr= 0.0m and tr =0.000s the cops at rest see Derick leaving the back of the train and head towards the front of the train on his relativistic car. The cops see him arrive at the front at xr = 1.875*10^5m...

I am working through Lessons in Particle Physics by Luis Anchordoqui and Francis Halzen. The link is https://arxiv.org/PS_cache/arxiv/pdf/0906/0906.1271v2.pdf. I am on page 21. Between equations (1.5.53) and (1.5.54), the authors make the following statement: ##S^\dagger ( \Lambda ) = \gamma ^0...

So I am working through Lessons in Particle Physics by Luis Anchordoqui and Francis Halzen, the link is https://arxiv.org/PS_cache/arxiv/pdf/0906/0906.1271v2.pdf I am in the discussion of the Dirac equation, on page 21, trying to go from equation 1.5.49 to 1.5.51. And I get stuck. Equation...

Homework Statement q,p transforms canonicaly to Q,P where given Q=q(t+s)+(t+s)p ,t is time and s is constt To find P Homework Equations Poisson bracket {Q,P}qp=1 The Attempt at a Solution Using Poisson bracket I find (t+s)*(dP/dp-dP/dq)=1

For example, Lorenz transformation of time means That measurement of time changes from one observer to another. I have read that this means moving clocks run slower. But this can't be true because Lorenz transformation of time depends on both of the seed of the observer and the object he...

Many discussions cite CP transformation as the exchange of particles for anitparticles. But other places it says that charge conjugation alone is sufficient to turn a particle into its antiparticle. So, the question is, when you exchange particles for anitparticles, is it a CP transformation or...

Homework Statement In a reference frame ##S## there is a particle with mass ##m## and charge ##q## which is moving with velocity ##\vec{u}## in an electric field ##\vec{E}## and in a magnetic field ##\vec{B}##. Knowing the relativisitc laws of motion for a particle in an EM field, find the...

I currently styding applications of Lie groups and algebras in quantum mechanics. U^{\dagger}(R)V_{\alpha}U(R)=\sum_{\beta}R_{\alpha \beta}V_{\beta} Where ##U(R)## represents rotation. Letter ##U## is used because it is unitary transformation and ##R_{\alpha \beta}## matrix elements of matrix...

Homework Statement I am asked to show that E[\exp(a*W_t)]=\exp(\frac{a^2t}{2}) Let's define: Z_t = \exp(a*W_t) W_t is a wiener process Homework Equations W_t \sim N(0,\sqrt{t}) The Attempt at a Solution I want to use the following formula. if Y has density f_Y and there's a ral function g...

Homework Statement With respect to a given Cartesian coordinate system S , a vector A has components Ax= 5 , Ay= −3 , Az = 0 . Consider a second coordinate system S′ such that the (x′, y′) x y z coordinate axes in S′ are rotated by an angle θ = 60 degrees with respect to the (x, y) coordinate...

What does it means for a physical theory to have hamiltonian, if it is formulated in lagrangian form? Why doesn't someone just apply the lagrangian transformation to the theory, and therefore its hamiltonian is automatically gotten?

Homework Statement I have attached the question. Translated: Suppose T: R^4 -> R^4 is the image so that: ... Homework Equations So I did this question and my final answers were correct: 1. not surjective 2. not injective. My method of solving this question is completely different than the...

Books say 3 possibilities for this situation as insert within Lacz, insert outside Lacz, no inserted vectors, then these goes the transformation with Ecoli. But we can't know transformation yield %100. Thus, if we make blue white screening there is more possibilities. Lacz-- inserted within...

Hi. If we want cell to accept vector dna in transformation, we treated with calcium chloride or chilled on ice etc.. But i have a trouble with one issue about that. Books say that ; We must choose the vector that specific according to the cell that will do transformation. But we will treat with...

Homework Statement Show, by completing the square in the exponent, that the Fourier transform of a Gaussian wavepacket ##a(t)## of width ##\tau## and centre (angular) frequency ##\omega_0##: ##a(t)=a_0e^{-i\omega_0t}e^{-(t/\tau)^2}## is a Gaussian of width ##2/\tau##, centred on ##\omega_0##...

Homework Statement Consider following transformation: Transformation: $$X^{\mu}\rightarrow \tilde{X^{\mu}}= X^{\mu}+\xi^{\mu}(\eta, \vec{x})$$ where ##\xi^0=T, \xi^i=L_i## Show transformation of metric perturbation ##B_i\rightarrow \tilde{B_i}=B_i+\partial_iT-\partial_{\eta}L_i## Homework...

In the momentum representation, the position operator acts on the wavefunction as 1) ##X_i = i\frac{\partial}{\partial p_i}## Now we want under rotations $U(R)$ the position operator to transform as ##U(R)^{-1}\mathbf{X}U(R) = R\mathbf{X}## How does one show that the position operator as...

Homework Statement An electric dipole instantaneously at rest at the origin in the frame K' has potentials \Phi'=\mathbf{p}\cdot\mathbf{r}'/r'^3 and \mathbf{A}'=0 (and thus only an electric field). The frame K' moves with uniform velocity \mathbf{v}=\vec{\beta }c in the frame K. Show that in...

Homework Statement Let ##T:ℝ^3→ℝ^2## be the linear transformation defined by ##\begin{bmatrix} x_1 \\ x_2 \\ x_3 \end{bmatrix}\mapsto \begin{bmatrix} x_1 + x_2 + x_3\\ 0 \end{bmatrix}##. i. Find the standard matrix for ##T##. Homework EquationsThe Attempt at a Solution For this problem I was...

Hi Forum I am trying to get a better grasp of the relation between electric field and the magnetic field. The overall question is "What is The origin of selfinductance in a current loop?" Here are my thourghts: A battery is connected to a say circular wire with some resistance. The current...

Homework Statement Homework EquationsThe Attempt at a Solution I have attempted and completed all questions. However, I am now trying part (b) with transforming the voltage source into a current source. I am unable to work out the current and I am unsure what to do next. I have included my...

Hi everyone! Sorry for my bad English! Please, suppose you have a subject A that opens his arms like a "T", in each hand he holds a laser and shoots the light at the same time. There are 2 targets at the same distance and, to A, the light hits both targets simultaneously. I Know that in some...

Dear all, As part of my MSc thesis I am using molecular dynamics simulation to study the pseudoelastic effect of Cu-Zr shape memory alloy during a tensile and shear tests. My question is related to the stress induced phase transformations during both tests. During the tensile test I can...