Conjugate Definition and 247 Threads

I've searched for this but found nothing,so I ask it here. What are canonically conjugate operators? Is [A,B]=cI a definition for A and B being canonically conjugate? Thanks

Momentum and position are canonically conjugate in physics because they are the Fourier transforms of each other. In the context of abstract algebra what would that mean. More precisely, Let G be the group they both (p and x) belong to and let ψ:G->G/H be the natural homomorphism where H is...

Hello, Let's have a group G and two subgroups A<G and B<G such that the intersection of A and B is trivial. I consider the subgroup \left\langle A^B \right\rangle which is called conjugate closure of A with respect to B, and it is the subgroup generated by the set: A^B=\{ b^{-1}ab \;|\; a\in...

The problem is to show sin\overline{z} = \overline{sinz}. What I need is help to get going.We know that sinz = \frac{e^{iz}-e^{-iz}}{2i}I can't see the first step in this. What I've tried to do is expressing sin\overline{z} and \overline{sinz} in terms of the above equation, but I don't know...

(This is not a question I was given to solve, it is a question about the course notes.) Homework Statement In impedance matching, what is the next best method after the complex conjugate method? If the source has V_s and Z_s, what should Z_L be? V_s, Z_s, and Z_L are in series. Homework...

Homework Statement If a cubic equation, f(x) has a factor of (3+√2), then the conjugate of the factor, (3-√2) is also a factor for f(x). Homework Equations The Attempt at a Solution Just to confirm is that statement correct? I read it else where but i not sure is it correct or...

In Sakurai's Modern Quantum Mechanics, he develops the Dirac notation of bras and kets. In one part, he states (page 17): <B|X|A> = (<A|X^|B>)* = <A|X^|B>* where X^ denotes the Hermitian adjoint (the conjugate transpose) of the operator X. My question is, since a bra is the conjugate...

The reason I ask the aforementioned question is because I came across the expectation values of operators in Quantum Mechanics. And part of the computation involves integrating a function of the complex conjugate of x with respect to dx. So as an example let's say I have: ∫ sin (x*) dx where...

Suppose E and D are both finite extensions of F, with K being the Galois closure of \langle D,E \rangle (is this the correct way to say it?) Is it correct that E and D are conjugate fields over F iff G,H are conjugate subgroups, where G,H\leqslant \text{Aut}(K/F) are the subgroups which fix...

For the last step in the derivation of the Gross-Pitaevskii equation, we have the following equation 0=\int \eta^*(gNh\phi+gN^2\phi^*\phi^2-N\mu\phi)\ dV+\int (N\phi^*h+gN^2(\phi^2)^*\phi-N\mu\phi^*)\eta\ dV, where \eta is an arbitrary function, g,N,\mu are constants, h is the hamiltonian for...

Homework Statement Consider the set ##C^2= {x=(x_1,x_2):x_1,x_2 \in C}##. Prove that ##<x,y>=x_1 \overline{y_1}+x_2 \overline{y_2}## defines an inner product on ##C^2## Homework Equations The Attempt at a Solution ##<,y>=\overline {<y,x>}## ##= \overline {y_1x_1} +...

First post! Is it true that for a complex function f({z},\overline{z}) \overline{\frac{∂f}{∂z}} =\frac{∂\overline{f}}{∂\overline{z}} I think I proved this while trying to solve a problem. If it turns out it's not true and I've made a mistake, I'll upload my 'proof' and have the mistakes...

Hey guys, I'm doing a third year course called 'Foundations of Quantum Mechanics' and there's this thing in my notes I don't quite get. I was hoping to get your help on this, if you don't mind. It's about Hermitian conjugate operators. The sentences go (v, Au) = (A†v|u) <v|A|u> = <v|(A|u>)...

Homework Statement Find all solutions to z^2 + 4conjugate[z] + 4 = 0 where z is a complex number. Homework Equations Alternate form: 4conjugate[z] + z^2 = -4 The Attempt at a Solution I have tried solving this solution using the quadratic formula. However, √b^2 - 4ac = √16 - 4x1x4 = 0...

Homework Statement suppose f and g are conjugate show that if p is an attractive fixed point of f(x), then h(p) is an attractive fixed point of g(x). Homework Equations f and g being conjugate means there exist continuous bijections h and h^-1 so that h(f(x)) = g(h(x)) a point p...

Homework Statement Show that the following = 0: \int_{-\infty}^{+\infty} \! i*(\overline{d/dx(sin(x)du/dx})*u \, \mathrm{d} x + \int_{-\infty}^{+\infty} \! \overline{u}*(d/dx(sin(x)du/dx) \, \mathrm{d} x where \overline{u} = complex conjugate of u and * is the dot product. 2. Work so far...

Homework Statement http://i43.tinypic.com/nxvw41.jpg Ok here it is molecule B. http://i39.tinypic.com/333aaro.jpg Ok and here it is problem nr. 8, second molecule. Homework Equations No equations needed. The Attempt at a Solution 1) So why is it that we do not add any...

if the wave function ψ(x)=R(x)eikx then what is it conjugate, ψ*?

I am not sure what the derivative with respect to a complex conjugate is and I have not been able to find it in any books. I assume I should use the chain rule somehow to figure this out: \frac{\partial z}{\partial z^*}, \quad z=x+iy Maybe you can do like this? \frac{\partial...

Homework Statement If P(x) is a polynomial with real coefficients, then if z is a complex zero of P(x), then the complex conjugate \bar{z} is also a zero of P(x). Homework Equations Book provides a hint: assume that z is a zero for P(x)=a_{n}x^{n}+a_{n-1}x^{n-1}+...+a_{1}x+a_{0} and...

I'm reading about symmetries in QM in "Geometry of quantum theory" by Varadarajan. In one of the proofs, he refers to theorem 2.1, which is stated without proof. He says that the theorem is proved in "Linear algebra and projective geometry" by Baer. That isn't very helpful, since he doesn't even...

Homework Statement let f(x) = x3 and g(x) = x - 2x3. Show there is no homeomorphism h such that h(g(x)) = f(h(x)) Homework Equations Def let J and K be intervals. the function f:J->K is a homeomorphism of J onto K if it is one to one, onto, and both f and its inverse are...

This isn't really a homework problem, just a form of writing I don't quite understand. The Dirac equation is: ("natural units") (i\gamma^{\mu}\partial_{mu}-m)\Psi = 0 When I try to build the conjugated equation, where \bar{\Psi} := \Psi^{+}\gamma^{0}, I get...

Homework Statement 1x2 Matrix A = [(5) (-2i)] What is the complex conjugate and Hermitian conjugate of this matrix? Homework Equations The Attempt at a Solution D^T = 5 -2i D^H = 5 +2i What do you think of my answers?

Hello all, I am trying to figure out how to solve for the complex conjugate of the following: (-0.5)^abs(x) Thanks for your help. -Brian

Hello, I'm having a problem finding the minor and major axsis lengths of an ellipse from three points, the ellipse's center, and two conjugate end point diameters. I have no problem solving the problem when the conjugate diameters align with the minor and major axsis, but when they don't the...

to get a Complex Conjugate of a #, is it ok to just replace i by -i even in denominator or inside argument?

I was trying to find the derivative of \overline{x} for some x \in \mathbb{C} I solved this as \frac{\mbox{d}}{\mbox{d}x} \left(\overline{x}\right) = \lim_{h \rightarrow 0}\frac{\overline{x+h}-\overline{x}}{h} \frac{\mbox{d}}{\mbox{d}x} \left(\overline{x}\right) = \lim_{h...

Hello, Differentiability of f : \mathbb C \to \mathbb C is characterized as \frac{\partial f}{\partial z^*} = 0. More exactly: \frac{\partial f(z,z^*)}{\partial z^*} := \frac{\partial f(z[x(z,z^*),y(z,z^*)])}{\partial z^*} = 0 where z(x,y) = x+iy and x(z,z^*) = \frac{z+z^*}{2} and...

Homework Statement See problem number 2 as attached. The Attempt at a Solution I found the reactions and shear and moment diagrams for the original beam. I also drew the conjugate beam and loaded it with M/EI. My only question for this problem is what the 4EI and EI under the beam...

Homework Statement Construct the slope and deflection diagrams. I've attached the problem with the original diagram (problem #1). The Attempt at a Solution Considering the number of diagrams required, I thought it would be best to attach a photo of my work. I drew the shear and moment...

[Linear Algebra] Finding T* adjoint of a linear operator Homework Statement Consider P_1{}(R), the vector space of real linear polynomials, with inner product < p(x), q(x) > = \int_0^1 \! p(x)q(x) \, \mathrm{d} x Let T: P_1{}(R) \rightarrow P_1{}(R) be defined by T(p(x)) = p'(x) +...

Homework Statement Find the hermitian conjugates, where A and B are operators. a.) AB-BA b.) AB+BA c.) i(AB+BA) d.) A^\dagger A Homework Equations (AB)^\dagger =B^\dagger A^\dagger The Attempt at a Solution Are they correct and can I simplify them more? a.)...

Homework Statement a.) Show \hat {(Q^\dagger)}^\dagger=\hat Q , where \hat {Q^\dagger} is defined by <\alpha| \hat Q \beta>= <\hat Q^ \dagger \alpha|\beta> . b.) For \hat Q =c_1 \hat A + c_2 \hat B , show its Hermitian conjugate is \hat Q^\dagger =c_1^* \hat A^\dagger + c_2^* \hat...

Homework Statement Okay so I've got a question I really need answered first up! If I have a 2x1 matrix for Psi, is Psi* a 1x2 matrix with all the 'i's turned to '-i's? Now onto the actual question - http://imgur.com/3ucb4" - part b only Homework Equations http://imgur.com/bcEm3"...

I need to show that u^{+}_{r}(p)u_{s}(p)=\frac{\omega_{p}}{m}\delta_{rs} where \omega_{p}=\sqrt{\vec{p}^2+m^{2}} [itex]u_{r}(p)=\frac{\gamma^{\mu}p_{\mu}+m}{\sqrt{2m(m+\omega_{p})}}u_{r}(m{,}\vec{0})[\itex] is the plane-wave spinor for the positive-energy solution of the Dirac equation...

Homework Statement Find all complex solutions to z^2 = z conjugate i.e. (a+bi)^2 = a-bi The attempt at a solution First attempt: factoring out (a+bi)^2 = a-bi leads nowhere. Second attempt: r^2 (cos2v + isin2v) = r (cos-v + isin-v) r must be 1. 2v = -v + 2∏n 3v = 2∏n v= 2∏n/3...

Homework Statement Show that f(z) = ¯z is not differentiable for any z ∈ C. Homework Equations The Attempt at a Solution Is it because the Cauchy-Reimann Equations don't hold? Z (conjugate) = x-iy u(x,y)=x v(x,y=-iy du/dx=1≠dv/dy=-1 du/dy=0≠-dv/dx=0 Edit: Is there another approach? Because...

Homework Statement Suppose x_{1} = \begin{pmatrix} 2 & 9 & 6 \\ \end{pmatrix}\begin{pmatrix} 3 & 5 & 8 \\ \end{pmatrix}\begin{pmatrix} 4 & 7 \\ \end{pmatrix} and x_{2} = \begin{pmatrix} 1 & 5 & 9 \\ \end{pmatrix}\begin{pmatrix} 2 & 7 & 6 \\ \end{pmatrix}\begin{pmatrix} 3 & 4 \\...

My textbook claims that the complex conjugate operator is linear. I can't see how this could be. Could someone give me an example of how it is not linear?

Homework Statement How would I go about proving that if K = gHg-1, for some g \inG, where K and H are both subgroups of G with a prime number of elements, then K = H? Homework Equations I've tried to prove it by saying that if K = gHg-1 then Kg = gH, and since H = gHg-1, then Hg = gH...

When you have i*e^(i@) as an amplitude, when you conjugate, do both i terms switch signs? I tried this and keep getting wrong answer. Thanks in advance. BTW this has to do with spin half particles.

I noted that if [itex]f : C \to C[\itex] is holomorphic in a subset [itex]D \in C[\itex], then [itex]\nabla \by \hat{f} = 0, \nabla \dot \hat{f} = 0[\itex]. Moreover, those two expressions are equivalent to the Cauchy-Riemann equations. I'm rewriting this in plaintext, in case latex doesn't...

Homework Statement Ive been given a question that requires an answer in polar form but the method I must use is the normal addition/subtraction of fractions. This throws me because I'm sure there is a simple method for the reciprocal of a complex number. Q. 1/(13- 5i) - 1/(2-3i)...

What's the complex conjugate of \frac{1}{\sqrt{1+it}}, \quad t \geq 0.

I've been reading Ballentine, Chapter 1. Have I got this the right way around? Taking our inner product to be linear in its second argument and conjugate linear in its first, the (continuous?) conjugate space of a Hilbert space \cal{H} is the following set of linear functionals, each identified...

Hi, I was wondering if it is possible to adapt the conjugate gradient method (or if there's a variation of the method) for nonsymmetrical boundary value problems. For example, I want to solve something like a 2D square grid, where f(x)=0 for all x on the boundary of the square...

prob solved, thanks anyway

divide complex number by conjugate. 1+3(sqrt-1)/ 2+(sqrt-1) The answer that i get is (5i/5)+1. Is this correct?

what is the difference between canonical and conjugate momentum.. ? what is its physical significant.. I was reading classical mechanics by Goldstein but could understood this terms