Conjugate Definition and 247 Threads

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?

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...

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)

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...

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...

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...

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...

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?

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...

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

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 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...

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

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...

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

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...

Im doing a bit of contour integration, and a question came up with a term in it am unsure of how to do: in its simplest form it would be \int\bar{z}dz where z is a complex number and \bar{z} is it's conjugate. Hmm i can't get the formatting to work out properly.. :S

Hey all, I was just curious: Why is the conjugate of a complex number (a + bi) defined as (a - bi)? If we instead change the sign of the real part (-a + bi), we still get a real number when we multiply the two. Is there a particular significance to the current definition...

I was working on some dark field filters and I was wondering if you could substitute the black spot in the centre of a dark field filter for a completely black filter with a light passing hole in the middle. Sort of an inverted dark field filter. I seem to remember reading something like this...

multiplying by a conjugate?? Homework Statement I am dealing with a limit, however, I am not sure how to multiply by a conjugate when there are two variables and three terms on top. For example lim [3h + sqrt( 2x +2h) - sqrt( 2x)] / h h->0 i don't need help solving it, i just...

pretty simple question. have to prove \hat{O} \hat{O}\dagger is a Hermitian operator. i found that \left( \int \int \int \psi^{\star}(\vec{r}) \hat{O} \hat{O}^{\dagger} \phi(\vec{r}) d \tau \right)^{\star} = \int \int \int \phi^{\star}(\vec{r}) \hat{O}^{\dagger} \hat{O} \phi(\vec{r}) d...

Homework Statement I want to show that \exp \left( i\bar{z} \right) = \overline{\exp \left( iz \right)} if and only if z = n\pi for any integer n. Homework Equations The Attempt at a Solution Utilizing Euler's formula, I got \cos \bar{z} = \cos z and...

$\lim_{x\to 1}\frac{\sqrt{x}-1}{x-1}$ Homework Statement Calculate the limit of \lim_{x\to 1}\frac{\sqrt{x}-1}{x-1}. Homework Equations As above. The Attempt at a Solution Have tried to multiplicate with the conjugate.

Homework Statement Consider 1L of a solution that is 0.100 M in acetic acid and 0.100 M in sodium acetate. What will the pH be, when 0.0900 mol of sodium acetate are added? Ignore changes in volume. acetic acid pka = 1.75 E-5 Homework Equations HA --> H+ + A- pH=pka +log A-/HA...

Homework Statement Prove that z_n -> z_0 if and only if ~(z_n) -> ~(z_0) as n goes to infiinity. ~(z_n) is the conjugate of z_n. Homework Equations The Attempt at a Solution |~(z_n) - ~(z_0) | = | ~(z_n) + ~(-z_0)| <= |~(z_n)| + |~(-z_0) | = |z_n| + |z_0| <= and I...

x''+x'+2x=0 x(0)=2 x'(0)=0 I've taken the characteristic equation and reduced the roots to 1/2 +- Sqrt(7/4)i of the form a +- bi (i = sqrt(-1) Then i put the homogeneous solution into the form of e^{}at*(B1cos(bt)+B2sin(bt)) for B1 i used the first i.c. and found that B1=2...

my question is what is meant by saying that A and B are similar where A and B are nxn matrices with entries in field F, also show that is A~B then A^2~b^2 first bit i have the definition for A~B is they are nxn matrices in the same field and there exists a non-singular square matrix P such...