What is Conjugate: Definition and 259 Discussions

A conjugate acid, within the Brønsted–Lowry acid–base theory, is a chemical compound formed when an acid donates a proton (H+) to a base—in other words, it is a base with a hydrogen ion added to it, as in the reverse reaction it loses a hydrogen ion. On the other hand, a conjugate base is what is left over after an acid has donated a proton during a chemical reaction. Hence, a conjugate base is a species formed by the removal of a proton from an acid, as in the reverse reaction it is able to gain a hydrogen ion. Because some acids are capable of releasing multiple protons, the conjugate base of an acid may itself be acidic.
In summary, this can be represented as the following chemical reaction:

Acid + Base ⇌ Conjugate Base + Conjugate Acid

Johannes Nicolaus Brønsted and Martin Lowry introduced the Brønsted–Lowry theory,
which proposed that any compound that can transfer a proton to any other compound is an acid, and the compound that accepts the proton is a base. A proton is a nuclear particle with a unit positive electrical charge; it is represented by the symbol H+ because it constitutes the nucleus of a hydrogen atom, that is, a hydrogen cation.
A cation can be a conjugate acid, and an anion can be a conjugate base, depending on which substance is involved and which acid–base theory is the viewpoint. The simplest anion which can be a conjugate base is the solvated electron whose conjugate acid is the atomic hydrogen.

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  1. Rasalhague

    Continuous dual space and conjugate space

    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...
  2. S

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    Homework Statement Hi all, I am trying to think of some intermediate (C,Java, Matlab) project ideas that would use the conjugate gradient, least squares regression (basiaclly a lot of statistical inference methods), lasso regression, and neural network feedback in order for a computer...
  3. I

    Conjugate gradient for nonsymmetric problem

    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...
  4. P

    If every two maximal subgroups of G are conjugate in G, prove that G is cyclic.

    1. Homework Statement Let G be a group in which each proper subgroup is contained in a maximal subgroup of finite index in G. If every two maximal subgroups of G are conjugate in G, prove that G is cyclic. 2. Homework Equations This problem arises as the problem #6 in section 5.4 of...
  5. J

    Divide complex number by conjugate.

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

    MATLAB Help on conjugate gradient programm in matlab

    hi 1.i have a problem to find the princip to programm in MATLAB the method of conjugate graduate, in fact ,my broblem is: 1.i want to study caracterisque of charge RC WHICH function is :y=a*(1-exp(b*t)) ,a is supposed to be tension maximal and b =1/RC the problem is that i have to find the...
  7. I

    Canonical and conjugate momentum

    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
  8. C

    Find Complex Conjugate of Wave Function in QM Mechanics Book

    I saw in a QM mechanics book the following wave function: psi(x) = A*[1 - e^(ikx)] what is the complex conjugate of this wave function? isnt it just psi*(x) = A*[1 - e^(-ikx)] but when you multiply psi(x) by psi*(x) shouldn't you get a real value? How come I don't?
  9. J

    Symmetry of Young's Tableaux with conjugate representation

    This isn't an assigned problem, just a popular forum I was hoping someone here would be able to help or move it to where it should be... Homework Statement I was working out the Young's tableaux for two SU(3) representations where 3 \otimes 3 = 6 \oplus \bar{3}, where the 6 is symmetric...
  10. P

    How can I find the determinant of the conjugate matrix?

    Homework Statement Homework Equations complex conjugate of a+bi is a-bi The Attempt at a Solution I defined M = A+Bi, where A and B contain real number entries. So that means that \bar{}M = A-Bi. Past that point, I don't know what to do. How can I find the determinant of the...
  11. M

    Complex Conjugate applied to operators?

    I have a rather fundamental question which I guess I've never noticed before: Firstly, in QM, why do we define the expectation values of operators as integral of that operator sandwiched between the complex conjugate and normal wavefunction. Why must it be "sandwiched" like this? From...
  12. Z

    Conjugate transpose/real and imaginary parts

    In my linear algebra text it says it's possible to define (for nxn matrix A) A_1^* =\frac{A+A^*}{2} A_2^* =\frac{A-A^*}{2i} so A=A1+iA2 It then asked if this was a reasonable way to define the real and imaginary parts of A. Is there a specific convention to define the real and imaginary parts...
  13. tom.stoer

    SU(n) - conjugate representation

    Very simple question, but I can't find the answer. Taking an su(n) Lie algebra with hermitean generators we have [T^a, T^b] = if^{abc}T^c One immediately finds that the new generators \tilde{T}^a = (-T^a)^\ast define the same algebra, i.e. fulfil the same commutation relations...
  14. C

    Is the Conjugate of a Polynomial the Same as Its Conjugate Field?

    Let p(x)=a0+a1x+a2x2\in Real Numbers and let z\in Complex Field. Show that p(conjugate of z)=conjugate of p(z)
  15. R

    Mathematica Mathematica Conjugate of a Function Assuming Real Variables

    Hi All, In mathematica, I'm trying to use Conjugate[] to take the complex conjugate of a function that has imaginary numbers in it, but I want to tell mathematica that the variables are real and positive, so that it can nicely combine terms into, say, x^2 instead of x*x. I've tried doing...
  16. J

    Complex conjugate of the expectation value of momentum

    Homework Statement Compute the complex conjugate of <p> using eq 1.35 (<p>=∫ψ*(h/i)∂/∂x ψ dx) and prove that <p> is real (<p>=<p>*) Homework Equations equation 1.35 is given above The Attempt at a Solution to take the c.c. don't i just add a minus to the i and switch the stars like...
  17. R

    Partial derivative with respect to complex conjugate

    So, my complex analysis professor defined \partial f / \partial z^* as \frac {\partial f}{\partial z^*} = \frac {1}{2} \left( \left(\frac {\partial u}{\partial x}-\frac {\partial v}{\partial y}\right) + i\left(\frac {\partial u}{\partial y} + \frac {\partial v}{\partial x}\right)\right) where z...
  18. A

    Complex conjugate zeros in pure RC ckt

    Hi, Is there a possibility of getting a complex conj zeros in pure RC ckt. we never get complex conj poles but how about complex conj zeros. regards, Asif
  19. R

    The conjugate of a Wave-Function

    I'm trying to show that the amplitude (A) of the wavefunction for a particle in a box is: A = sqrt(2/L) : L is the length of the box. I'm using \psi(x) = Asin ((n*pi*x) / L) as the wave equation. To do this I'm trying to integrate the probabilty density function from 0 through to L...
  20. J

    Heisenberg uncertainty principle derivation and canonically conjugate vairables?

    Hi, I've just worked through a derivation of the H.U.P. that uses the Cauchy Schwarz inequality to come up with the expression (\Delta A)^2(\Delta B)^2 \geq \frac{1}{4}|<[A,B]>|^2 . This much I am happy with, but then it seems that when dealing with two "canonically conjugate observables" you...
  21. L

    Hermitian conjugate of spinor product (Srednicki ch 35)

    Hi, I totally understand why \chi\psi=\chi^{a}\psi_{a}=-\psi_{a}\chi^{a}=\psi^{a}\chi_{a}=\psi\chi. Where the first equality is just convention, the second is anticommutation of the fields, the third is due to \chi^{a}\psi_{a}=-\chi_{a}\psi^{a} because of the \epsilon^{ab} . But now if...
  22. S

    Preconditioned conjugate gradient method

    Hi, I've gotten the conjugate gradient method to work for solving my matrix equation: http://en.wikipedia.org/wiki/Conjugate_gradient_method Right now I'm experimenting with the preconditioned version of it. For a certain preconditioner however I'm finding that is zero, so no proper update...
  23. S

    Modern Algebra-Proving Elements Conjugate

    1. If a1,...,an is a list of (not necessarily distinct) elements of a group G, then, for all i, ai...ana1...ai-1 is conjugate to a1,...,an. Homework Equations The Attempt at a Solution I know that you have to prove the existence of an element g of the group G such that...
  24. X

    Derivative of a complex conjugate?

    Homework Statement [PLAIN]http://img823.imageshack.us/img823/4500/85131172.png Homework Equations Derivations and substitutions. The Attempt at a Solution Basically it seems like a very simple problem to me however I can't seem to get the right answer. First I just assumed that the c.c...
  25. A

    Why do we need to take the conjugate in complex power calculations?

    Ive seen in some situations the equation S=VI is being used with the conjugate of I IN what situations do you have to take the conjugate and why?
  26. W

    Which is the conjugate variable?

    take a 1/2 spin, that is, a qubit the general state is of the form psi= \cos(\theta /2) |g>+ e^{i\phi} \sin(\theta/2) |e> where |g> and |e> are the two basis states it is stated in a PRL paper that \phi is the conjugate variable to \sin^2(\theta/2) why? by the way, for a 1/2...
  27. P

    Coordinate conjugate to momentum.

    Let's take a system, for simplicity with only one degree of freedom, described by a certain lagrangian L[x,\dot x] I define the momentum p=\frac{\partial L}{\partial\dot x} Now, if I make a change of coordinates x\longmapsto y\qquad\qquad\qquad(1) I obtain a second lagrangian M[y,\dot...
  28. C

    The Conjugate Method for Limits

    I'm reviewing limits to tutor a student in precalc and came across a problem. The conjugate method multiplies the numerator and denominator by the conjugate of the numerator or denominator to simplify the equation. However, after a quick example I wrote for myself, I found that: lim x-> 3...
  29. Simfish

    Is the conjugate gradient algorithm susceptible to getting into local minima?

    What about the nonlinear forms of it? Or is it guaranteed to reach a global minimum?
  30. M

    Conjugate momentum in the hamiltonian

    Hey, I just have a quick question that I haven't quite been able to find a definitive answer to, regarding conjugate momenta in the Hamiltonian. Ok, so it regards the following term for the hamiltonian in a magnetic field: H=\frac{1}{2m}(p-qA)^2 I'd like to ask whether p is the conjugate...
  31. A

    Conjugate Bases of NH2-: Identifying

    Homework Statement Indicate the conjugate bases of the following: NH2- NH2- Homework Equations The Attempt at a Solution This is the only information given. Can I assume that these species react with water? The ionic signs indicate that they are bases, but are they the...
  32. M

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    Homework Statement Let u(x,y) be harmonic in a simply connected domain \Omega. Use the Cauchy-Riemann equations to obtain the formula for the conjugate harmonic v(x,y)=\int^{(x,y)}_{x_0,y_0} (u_xdy-u_ydx) where (x_0,y_0) is any fixed point of \Omega and the integration is along any path...
  33. W

    Prove Complex Conjugate: z=cisθ

    Homework Statement i am supposed to prove that for the complex number z=cis\theta the conjugate is \frac{1}{\overline{z}} Homework Equations if z=a+bi \overline{z}=a-bi The Attempt at a Solution all that i can think of is that \frac{1}{cos\theta i sin \theta} =(cos \theta i sin...
  34. L

    STRACT: Understanding the Complex Conjugate of a Function

    Homework Statement I have a complex function w\left(z\right)=e^{sin\left(z\right)} What is the conjugate? 2. The attempt at a solution The conjugate is w\left(z^{*}\right)=e^{sin\left(z^{*}\right)} w\left(x-iy\right)=e^{sin\left(x-iy\right)} My question is, is my answer...
  35. maverick280857

    Charge Conjugate Dirac Field

    Hi, I'm trying to work my way through Halzen and Martin's section 5.4. I'd appreciate if someone could answer the following question: How does j^{\mu}_{C} = -e\psi^{T}(\gamma^{\mu})^{T}\overline{\psi}^{T} become j^{\mu}_{C} = -(-)e\overline{\psi}\gamma^{\mu}\psi ? Is there some...
  36. zonde

    Probability is square of amplitude or it's product with complex conjugate?

    I have seen discussion about it here but it is still not clear to me whether probability is square of probability amplitude or is it product of amplitude with it's complex conjugate. I looked in HyperPhysics http://hyperphysics.phy-astr.gsu.edu/Hbase/quantum/qm.html#c5" and it says it's product...
  37. S

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  38. K

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    I'm working on a control theoretical problem and trying to implement the solution in Matlab. Part of the solution requires minimizing a function f(x), for which my predecessor has opted to use a conjugate gradient method. He wrote his own conjugate gradient method, but it's not converging. I've...
  39. D

    Why is the derivative of a complex conjugate zero in quantum mechanics?

    Hi. Sometimes in my quantum mechanics course we encounter derivatives such as \frac{d}{dz}z^*, i.e. the derivative of the complex conjugate of the complex variable z wrt z. We are told that this is just zero, even though I know that the complex conjugate is not an analytic function ... Has...
  40. W

    LaTeX Latex code for Hermitian Conjugate

    Hi there, Does anyone know the Latex code for Hermitian conjugate (dagger) on TeXniccenter? Thank you!
  41. B

    Finding a Complex Conjugate value of wave function

    First, sorry for my poor English and any impolite behavior might happen. Here's two wave function(pic1) and problem below(pic2). and they are polar coordinate problem ψ(r,θ,Φ) You can see, problem requires conjugate function of ψ1. Is it possible to find one? or is there a possibility...
  42. S

    The limit of the complex conjugate as z -> 0

    Hi I'm wondering if the z- (complex conjugate of z) goes to zero as z does? Also what is the derivative of z- with respect to z? Thanks
  43. Hepth

    Conjugate Transpose for a vector

    In particle physics, we commonly have the gamma matrices, whose conjugate transpose is the raised or lowered index. Does the same rule apply to ANY indexed quantity? What about to scalar/vectors like momentum. Is the conjugate of momentum: \left(q_\mu\right)^\dagger = q^\mu The...
  44. N

    How to Find the Conjugate of a Complex Exponential Function?

    Homework Statement Find the conjugate of \varphi=exp(-x^2/x_0^2) Homework Equations The Attempt at a Solution Isn't the conjugate \varphi*=exp(x^2/x_0^2)
  45. S

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  46. P

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  47. D

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  48. E

    Conjugate Homogeneity for Self-Adjoint Operators: Proof and Explanation

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  49. Pythagorean

    Non-adjoint Conjugate of Pure State Vector

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