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.
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...
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...
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...
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...
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...
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
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?
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...
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...
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...
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...
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...
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...
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...
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
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
I've been trying to prove something that seems obvious but have had no success thus far:
say G is a finite group and H and K are proper subgroups, if K contains a conjugate of H, then it isn't possible to have G=HK.
Proof anybody? I'm happy if one can prove the special case below:
It's...
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...
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...
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...
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...
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)
The pKa for the dissociation of H3PO4 is 2.15. What is the concentration of H2PO4-1 (in M) at pH 3.21 if the original concentration of the phosphate was 2.37 M?
My Attempt:
Key Information:
pH final: 3.21
Initial Molarity of phosphate: 2.37 M
pKa: 2.15
I started with the first...
Homework Statement
Supposing that A*B is defined (where A and B are both matrices in the field of the complex numbers), show that the conjugate of matrix A * the conjugate of matrix B is equal to the conjugate of A*B.
Homework Equations
None.
The Attempt at a Solution
I'm stuck. I've...
Hello,
Working without complex numbers a conjugate of any function in a LVS is always the same thing. A conjugate of any matrix in a LVS is very often not the same thing though. I am just confused as to why functional spaces rely on complex numbers for the conjugate to have any importance and...
(aT)∗ = \bar{a}T∗ for all a ∈ C and T ∈ L(V,W);
This doesn't make much sense to me. Isn't a supposed to be=x+iy and
\bar{a}=x-iy? Not a fan of complex numbers. And
this proof also confuses me.7.1 Proposition: Every eigenvalue of a self-adjoint operator is real.
Proof: Suppose T is a...
If I have a pure state vector of a system (let's call it A):
-0.4431 + 0.2317i
-0.4431 + 0.2317i
0.5000
0.5000
A particularly interesting symmetry in the system allows a similar pure state (B):
-0.4431 - 0.2317i
-0.4431 - 0.2317i
0.5000
0.5000
the absolute value of the inner...