Hi all.
The final project for my quantum optics class is to find a topic (research paper or something in the field of quantum optics) and present it to the class. The assignment implies that to give an effective presentation you have to understand the topic very well. This high level optics...
Thanks Galileo, I believe I have gotten the answer since E (non-vacuum state) is:
\hbar\omega n
We could just assume that \rho (n) = C*exp(- \hbar\omega n ) and then it is easy street from there on...
Actually I figured it out the answer to the mean: you can use the following expressions:
n\hat|n> = n|n>
n\hat|n+2> = n+2|n>
So, when it is all said and done the mean should be n + 1/2
Thanks a lot for the help!
Hey Galileo, thanks for the input. N is the observable that I believe corresponds to that measurement. I just don't know how to handle the |n+2> situation...
The Hamiltonian (ignores vacuum energy), H = \hbar\omega_{p}a_{p}^+a_{p} , represents some cavity at temperature T. For simplicity assume the cavity only supports a single mode.
H = \hbar\omega_{m} a_{m}^+ a_{m}
1) Given that in thermal equilibrium the probability of a system to have...
[b]1. So, here is the problem: Suppose the state of the field is described by a state vector->
|\psi> = \sqrt(3)/2|n>_{m} + 1/2|n+2>_{m}
( |n>_{m} means "n" photons in mode "m" and zero photons in every other mode)
If a measurement is made to determine th number of photons in mode "m"
a)...
YES! That's the operator expansion theorem that I couldn't find! Thank you so much meopemuk. And I truly appreciate your efforts \mu 3. Meopemuk, do you know this equation off the top of your head or can you recommend a book? My quantum optics prof. assumes we know QM but we're all engineers and...
theta is the angle that the squeeze state makes with one of the quadrature axes... I think it can be explained away by saying its absolute value is zero, but it's probably not that important. There is no tau; if you mean the 'r' in cosh(r), it is the displacement of the squeeze state or...
Homework Statement
I need to prove:
a'(z)=S(z)aS^\dagger(z)
Where S(z) is the squeeze operator and a'(z) is the pseudo-lowering operator.
Homework Equations
S(z)=e^{\frac{1}{2}({z^\ast}a^2-za^{\dagger 2})}
e^x=\sum_n{\frac{x^n}{n!}} ; I don't think 2 simultaneous Taylor...
Check out wikipedia at http://en.wikipedia.org/wiki/Perturbation_theory_(quantum_mechanics ). Under Time-dependent perturbation theory there is some helpful looking stuff. I think I might know how to put A into all this but I totally don't understand the step that get you to d cn/d t. It says...
I think this might have to do with perturbation theory. This homework is due in a few hours but even of you don't get around to answering by then I'd still like to know. Thanks.
Brilliant... that's very helpful... thank you very much.
Now for the other question; I think the state of a system evolves with
i\hbar \frac{\partial }{\partial t} \right)|\psi(t)> = H|\psi(t)>
That LaTeX code stuff is helpful, so I'm learning it as I go along... Anyway, I still don't know...
Yes! p = -i h bar d/dq. That's awesome! So, for the first one, -[f,p] = (-1/i h bar) (f p - p f) = (-1/i h bar)(f -i h bar d/dx - (-i h bar df/dx)) = f d/dx + df/dx! The second part of that is the answer, but what is f d/dx and how does it go away? Should I perhaps make all this stuff act on x...
Hey all-
I am new to quantum mechanics so these questions will be elementary and don't be afraid to go over simple concepts. There are two questions on the homework that I barely even know how to approach (I don't know how to type p sub k properly so that is how I will be writing it)...