Thank you for the reply. I have a doubt though. If you change variables such that ## cx + dy = z \Rightarrow y = \frac{z}{d} - \frac{cx}{d} \equiv pz - q, ## where ## q(x) = \frac{cx}{d} ## how can you do the x integral? Do you mean complete squares in the x variable and then inegrate? But...
Homework Statement
I want to evaluate the following definite integral of the form,
I = \int\limits_{x = -\infty}^{\infty}\int\limits_{y = -\infty}^{\infty} e^{-ax^2} e^{-by^2} | \cos(c x + d y)| dx dy
where a, b, c, and d are constants, as part of a larger problem I am doing,
Homework...
Homework Statement
I am trying to calculate the wigner function for the even coherent state or cat state gives by,
| \psi \rangle = N_+ \left( |\alpha \rangle + | -\alpha \rangle \right),
where ##|\alpha \rangle ## is a coherent state and ## |N_+|^2 = \dfrac{1}{ 2 + 2e^{-2|\alpha|^2}}##. I am...
Homework Statement
I ended up solving the problem as I was typing it up, I am posting what I did anyway as it took so long to type and might be useful to someone else.
I am trying to figure out the position representation of a coherent state and it's time evolution. I should be getting a...
For example let us take ##S_z## and systematically write down it's representation in the ##\{ |1,-1\rangle, |1,0\rangle, |1,1\rangle \}## basis. First of all we need to know the action of the operator ##S_z## on this basis. Since these states are eigenstates of the ##S_z## operator this is...
Yes! This seems to be the answer. If you see the effect of the unitarty on the entire system,
(\mathbb{1}_A\otimes U_{BC}) ( \rho_{AB} \otimes |0\rangle\langle 0 |_C ) (\mathbb{1}_A\otimes U_{BC}^{\dagger}) = \frac{1}{2} (|000\rangle\langle 000| + |111\rangle\langle 111| ) and a measurement of...
The no cloning theorem states that you cannot build a unitary to copy an arbitrary state. However you can still create one that copies known orthogonal states.
What you should understand is that when you write a matrix down for an operator such as you have done for ##S_z## and ## S_x ##, you have already chosen a basis to represent that operator in. In this case the basis you have written it in is ## | 1 -1 \rangle ## , ## | 1 0 \rangle ## and ## | 11...
As I understand it, faster than light communication is not possible, but I have a specific example which concludes that it is and I'm trying to find the mistake.
The scheme uses two things
1) An entangled Bell pair ## | \phi \rangle = | 0 0 \rangle + | 1 1 \rangle## ( neglecting normalization )...
I am trying to understand wick's theorem and normal ordering mostly from Peskin and Schroeder. Now I have this problem with how normal ordering is defined. It seems to me that if you take the normal ordering of a commutator it should always be zero.
Here is what I understand normal ordering to...
Could you elaborate a little? Are you saying that the observed experimental data rules out a further fine structure for elementary particles in the standard model? I know that the existence of quarks were confirmed from high energy scattering from nucleons. My question is with the current...
We say that spin is an intrinsic angular momentum which does not have anything to do with space. But is it possible that it is the orbital angular momentum of some internal constituent particles (a yet unknown fine structure)?
Also is there some criteria for an integral not to exist if the integrand is is infinite at some point? For example a delta function has a formal infinity in it, but the integral over a delta function is still well defined. Also what is the criteria for a point to be called a singularity? I have...
Thanks for all the replies...I think I understand now. I had thought it had something to do with the singularity at 0 but was unsure of how to deal with it. As I understand it, in this case even the Principle value diverges does it not? I often hear mathematicians say that an integral does not...
I am getting two different answers with two different methods so can someone point out the error?
\int\limits_{-\infty}^{\infty} \frac{1}{x^2}dx = 2 \int\limits_{0}^{\infty} \frac{1}{x^2}dx = - \frac{2}{x} |_{0}^{\infty} = \infty
\int\limits_{-\infty}^{\infty} \frac{1}{x^2}dx = -...