Conjugate Definition and 247 Threads

Why there is an uncertainty relation between conjugate variables? what exactly are conjugate variables?

Hi I have received PM so I would like to post this question for scientific debate here conjugate of every variable is denoted by _. 1.define f_:R3->R3 by f_(x_)=y_, where y1=x1+(x2)2+(x3-1)2, y2=(x1)2+x2+((x3)2-3.x3), y3=(x1)3+(x2)2+x3.prove that f_ is locally invertible about x_=(0,0,1)...

A wave function(psi) is a mathematical quantity which gives complete information about the state of a system at a particular instant of time. But what information does the complex conjugate of a wave function(psi*) give? Does it represent the same state as psi? Or does it just have a...

I have two questions Homework Statement Show that the function defined by complex conjugation is not differentiable. Homework Equations If z = x + iy then the complex conjugate of z is x - iy The Attempt at a Solution f'(z) = lim z -> z1 \frac{f(z) - f(z1)}{z - z1} So I...

What is the Hermitian conjugate of a complex #, say, 5+6i??

Hi today I will be constructing a ratio thing for math. Our teacher asked us to survey as many people as we can. I am going to ask a simple math question and if you can answer it with 100% confidence. This is just a little survey I am not trying to trick you in doing my homework, I already know...

Homework Statement Suppose that f(x) is a polynomial of degree n with real coefficients; that is, f(x)=a_n x^n+ a_(n-1) x^(n-1)+ …+a_1 x+ a_0, a_n,… ,a_0∈ R(real) Suppose that c ∈ C(complex) is a root of f(x). Prove that c conjugate is also a root of f(x) Homework Equations...

i was thinking this over, and i'd like to know if the following statement is valid: \oint\overline{z}dz = \oint1/zdz over the contour \left|z\right|=1 any thoughts?

Hi, Is there any trick to treat complex conjugate variables in polynomial equations as independent variables by adding some other constraint equation ? Say, we have polynomial equation $f(x,x^{*},y,...) = 0$. where x^{*} is the complex conjugate of variable $x$. I might think of taking $x = r...

Homework Statement sun, I don't know why I am stuggling with a simple freakin problem. Its not even for me its for my friend who's in college algebra, but for some reaon I can't get the correct answer. {9 - 11i \over 6i} The Attempt at a Solution I multiplied by the conjugate twice and...

It's very commong to use z and z* as two independent variables, differentiating with respect to one while keeping the other constant. Can you please give me some intuitive insight into this method, and why it works so well? Because every time I see this my first thought is that z and z* are NOT...

Hello All, As I understand it, the wavefunction Psi(x) can be written as a sum of all the particle's momentum basis states (which is the Fourier transform of Psi(x)). I was woundering if the wavefunction's complex conjugate Psi*(x) can be written out in terms of momentum basis states, similar...

Let F:H->R bar be a function and F*:H->R bar its conjugate. Fix aEH and show that the conjugate of the new function G(u)=F(u-a) is G*(u*)=F*(u*)+<a,u> Verify the case where F:R^2->R, F(x)=1/2(x)^2 and a = (2,-1) I don't really know how to show this. please help

Does an inverse exist for every quaternion under multiplication??

Show that the extermals of any functional of the form integ (a->b) F(x,y') dx have no conjugate points. Not sure how to start this question, any help would be appreciated

Homework Statement does (\sin{z})^* = \sin{z^*}? (where z is a complex number) Homework Equations \sin{z} = \frac{1}{2} (e^{iz} - e^{-iz}) The Attempt at a Solution (\sin{z})^* = \frac{1}{2} (e^{iz} - e^{-iz})^* = \frac{1}{2} (e^{-iz^*} - e^{iz^*}) = -\frac{1}{2} (e^{iz^*} - e^{-iz^*}) =...

Let A be a nxn matrix. Prove that if (A*)A=0 then A=0. What if A(A*) = 0? A* is the conjugate transpose of A. When I write out the expansion formula, I cannot conclude that every entry of A is zero. What am I missing?

Simple question, and pretty sure I already know the answer - I just wanted confirmation, Considering the Hermitian Conjugate of a matrix, I understand that A^{+} = A where A^{+} = (A^{T})^{*} Explicitly, (A_{nm})^{*} = A_{mn} Would this mean that for a matrix of A, where A is a...

Homework Statement a = x + \frac{d}{dx} Construct the Hermitian conjugate of a. Is a Hermitian? 2. The attempt at a solution <\phi|(x+\frac{d}{dx})\Psi> \int\phi^{*}(x\Psi)dx + <-\frac{d}{dx}\phi|\Psi> I figured out the second term already but need help with first term... am...

Homework Statement Show that the helicoid and the catenoid are conjugate minimal surfaces Homework Equations the helicoid is given by the parameterization X(u,v) = (asinh(v)*cosu, asinh(v)*sinu, au) = (x1, x2, x3) the catenoid is given by the parameterization Y(u,v) = (acoshv*cosu, a...

Homework Statement show that det(A)=(detA)*= det(A$) where * denotes complex conjugate and $ means transpose Homework Equations The Attempt at a Solution Please help me to start the problem.I am not getting a way.

I just have a simple question about hermition conjugates of spinors. Is the hermitian conjugate of: \epsilon \sigma^\mu \psi^\dagger equal to: -\psi \sigma^\mu \epsilon^\dagger where both psi and epsilon are 2-component spinors of grassmann numbers?

I'm studying abstract algebra and never got the hang of ideas like these. Currently I am trying to grasp: Show that the splitting field of a quadratic polynomial P(x) = Ax^x + Bx + C, with zeros \alpha and \alpha^{'} is V_\alpha = Q*1 + Q * \alpha. Q is of course the set of rationals. I...

I am working through this algebra book and some of the problems. The chapter this comes out of is General Algebraic Systems and the section is Isomorphisms. I am new to proofs and maths higher than calculus I so I am not sure if I am following the text or not. There aren't any solutions and this...

Need Assistance w/ existence of conjugate roots in polynomial Prove: given that f(x) = Anx^n + An-1X^n-1+ ...A1X + A0 , and An does not = 0 => if f(x) has a root of the form (A+Bi), then it must have a root of the form (A-iB). (complex roots) So far I've come up with the conjugate roots...

okay, so this particular equation involves me writing conjugate of either sin or cos, but hows that possible considering they both are real in the given problem? maybe i should convert sin and cos into their exponential form first? but then wt would be the conjugate of this...

Please help! -Dirac delta potential-, Hermitian Conjugate Im trying to solve problem 2.26 from Griffiths (1st. ed, Intro to Q.M.). Its about the allowed energy to double dirac potential. I came up with a final equation that is trancedental. (After I separate the even and odd solution of psi.)...

In the complex conjugate of an integral equal to the integral of the complex conjugate? If so, is there an easy way to show this? Thanks.

I would like to prove \mid z + \overline{z} \mid \leq 2 \mid z \mid The first way I could think of: \begin{multline} RHS^2 - LHS^2\\ =4\mid z \mid^2 - \mid z + \overline{z} \mid ^ 2\\ =4z\overline{z} - (z + \overline{z})(\overline{z}+z)\\ =4z\overline{z} -...

Which acid of the following set has the strongest conjugate base? a. CH4 b. NH3 c. H2O d. HF Is this correct? Any help is appreciated

1. Which Bronsted-Lowry acid has the strongest conjugate base? a. HBr b. HClO4 c. HF d. HI 2. What is the strongest acid among the following? a. HF b. HCl c. HBr d. HI Correct? Thanks.

I am perplexed. My professor told me that I can conjugate: \psi \left( x,0 \right) However, I am confused. There is no time dependence, there is no i. It is like saying z = a + 0i z* = a - 0i It is rather useless to even say that and it seems also useless to conjugate something with...

Is the the following definition correct? Two elements a and b of a group G are said to be CONJUGATE if there exists g in G such that a=gbg^{-1}. For instance, show that all elements in the symmetric group S5 of order 6 conjugate.

Hi everyone! How can I find the Hermitian conjugate of the differential operator D, with D psi = 1/i dpart/dpart(x) psi? I know you can do this with partial integration starting from <phi|D|psi>* = <phi|D+|psi> but how exactly does it work? I'm sorry for using such an ugly...

Uggh finally did all the chem problems and studied for the upcoming final but there are 2 questions left unanswered. MAybe someone can help me out with this: If given a lists of acids, how would one know which 1 is the weakest conjugate base? For example, HF, HNO_2, H_2CO_3, H_3BO_3, HCl...

I'm doing a take home final and wanted reassurance that I'm doing the problem right. the question involves taking <Sz>of |psi>. I know it's <psi|Sz|psi>. I've never done it for a spin 2 particle which is a 5*5 matrix.Do i just take the complex conjugate of the values without switching their...

How do you do it?

Whats the formula for this conjugate bases? how do I get them? a) HSO3tothe(-) b) NH3 c) HCL and how is the lewis acid and lewis base identified? thanks

Hi, Is there a general method, given \sigma and \rho in Sn, for finding a permutation \tau in Sn such that \rho = \tau ^{-1} \sigma \tau? I know how to do it when \sigma and \rho are made of a single k-cycle, but what happens when they are more complex? For example, for: \sigma = (1...

I'm guessing the answer is a). I found a similar problem except if the bicarbonate was mixed with water instead. And the selections were: H3O(+), OH(-), CO3(2-), H2CO3 I think the answer to that question would be H2CO3 since it's asking for the conjugate acid which will be the form of...

to make a 25mM buffer with pH5.2 i add 25mM ethanoic acid with 25mM sodium ethanoate. after adjusting the pH, the buffer will still be 25mM. will this also be the case if i use 25 mM Tris-base and 25 mM phosphoric acid? will i still get a buffer with 25mM after adjusting the pH to 5.2 with...

What is a conjugate hyperbola? I'm asked to find the equation of the conjugate hyperbola if the asymptotes are y = +/- 2x. Would it be \frac{x^2}{1} + \frac{y^2}{4} = 1 or \frac{x^2}{1} + \frac{y^2}{4} = -1?

Hello, I have to do a proof and am having trouble starting. The proof is to show how you could use Cholesky decomposition to determine a set of A-orthogonal directions. Cholesky decom. means I can write the symmetric positive definite matrix as A = GG' The textbook gives a way...

1) (-7+20)(-10-3i) 2) (-2-5i)/(3+4i) I don't think I did these two questions right does anyone know how?

Hi there. What is the conjugate acid of H2PO4. And what does it mean. H3PO4 or HPO4 I got it. It means when a base gains a hydrogen ION. H3PO4 is the right answer isn't it.

Difference between acid and conjugate acid :confused:

I am having trouble simplifying (4[(SQRT(x+2)) – (SQRT2))]/x I multiply the conjugate and I come up with 4/((SQRT(x+2)) + SQRT2) I'm not sure if I'm on the right track