You're saying this as if not having an infinite precision number is the only problem of having a perfect circle.
I think many students do this and confuse physics with math. There's a very thick line separating physics from math, and that's where you're wrong.
A circle is a mathematical...
@bigfooted Thank you very much. Your message made me feel much better. Would you provide me some help on the personal level? Since you work at a very similar thing as I do, you would know what I need to do to get started, and what I need to focus on. I'd appreciate it a lot. Can I PM you?
Dear readers:
I would like to share my story with you, and I really appreciate your advice.
I graduated last year from ETH Zürich as a PhD in physics. Now I'm doing a Postdoc in a group as my first step in a "science" career.
The Problem:
As much as I love research and enjoy doing science...
@vanhees71
I agree the asker asked an ambiguous question. The probability to be in state j is P_j=\langle \psi | o_j \rangle I would say. I think people learning QM always get confused because the concept of preparation of states isn't clear. I guess a logical question for a new learner is...
@vanhees71
I see. You're talking about the eigenvalues of the density matrix itself. I think the asker meant the eigenvalues of the Hamiltonian, which explains why he provided eigenvalues -1 and 1.
@vanhees71
Although this is an old post, but I really have to ask:
Why are you constructing the density matrix using the eigenvalues and not the probabilities? This makes it like if the eigenvalue has units of energy, the density matrix will have units of energy too... isn't the density matrix...
Thank you for your response, though I would like to tell you that definitely googling it is the first thing I have done, but it doesn't help, because apparently EMU has many different conventions and I'm looking for something specific used for magnetometer sensitivity.
Magnetometer sensitivity...
In many, many articles about the SQUID magnetometer, I see people referring to the sensitivity of the magnetometer in units of EMU, as in this article:
http://iopscience.iop.org/0268-1242/26/6/064006
or this
http://link.springer.com/article/10.1007%2FBF02570388
Could someone please explain...
Thanks to the people who've helped, though the problem was pointed to me by my Professor.
The problem was in the definition of raising and lowering operators with respect to spherical basis...
Thank you for your response. As reasonable as what you're saying sounds, I verified the signs like 5 times in different times to make sure there's no mistake, and I can't find any. Let me give an example. Let's talk about the z equation.
The equation is...
Thanks for your response. I checked it and I found no sign error; though maybe I'm wrong, but this is a secondary problem, since even if a sign error is there, this won't resolve the problem I'm facing where those equations have nothing to do with Bloch equations the way we know them.
Any...
This question was on Stackexchange, and no one was able to solve it. So now I'm posting it here, and I wish someone could help.
I'm trying to derive the Bloch equations[1] from the Liouville equation[2]. This should be possible according to this paper[3], where it discusses higher order Bloch...
Thank you for your answers, guys.
Like Kith said, I need to add components and not have the product. A 63*63 matrix is redundant, where it gives me, for example, a state | F=3,F=4,m_F=3,m_F=-4 \rangle, which is definitely wrong. What I'm doing is adding components... please consider...
If I do this product the result's side length will become 7*9=63 elements... while my combined system from F=3 and F=4 has only 7+9=16 elements, since F=3 has side-length 2*3+1=7 and F=4 has 2*4+1=9.
So here's the problem right now.
Thank you for your time. Wigner D-Matrix for that case will be the following, starting from the eigen-vector |F=3;m_F=-3 \rangle to |F=3;m_F=3 \rangle
D^{F=3}=\left(
\begin{array}{ccccccc}
e^{-3 i \alpha -3 i \gamma } \cos ^6\left(\frac{\beta }{2}\right) & -\sqrt{6} e^{-3 i \alpha -2 i \gamma...
Thank you, I appreciate your help so far. You could though (if you're interested) look at this further. Wigner-D matrices are simply the matrices that provide rotations in the angular momentum basis with Euler angles.
So you have a basis of F=3 and m_F=-3,...,3, the Wigner-D matrix will be...
Hmmmmmmm... Thank you so much. Though I thought this approach would solve my problem, but apparently it doesn't.
I have Hyperfine states with F=3,4 (where F=I+J is the sum of the total angular momentum and the nuclear spin), and I want to separate them, do a rotation with Wigner-D matrices, and...
Thank you so much for your answer. Let me though put an example to make this clear, because I got some result that I don't believe. Say I have the Hamiltonian matrices H_1 and H_2
H_1=\left(
\begin{array}{cccc}
\text{s1} & 0 & 0 & 0 \\
0 & \text{s2} & 0 & 0 \\
0 & 0 & \text{s3} & 0 \\
0 & 0...
I'm trying to solve a dynamical quantum mechanics problem related to the Cs atom, but I'm having trouble in the following, and I'm afraid I'm doing it wrong.
Say I have the matrix form of the Hamiltonian on a basis for a system | \psi \rangle to be H_\psi, and another system with bases |...
Thank you for your reply. I still have a little problem understanding how those two cases are equivalent physically.
You're telling me that both cases are equivalent up to a phase factor, but I see there's different physics there, because one gets different energy splitting/displacement...
I have angular momenta S=\frac{1}{2} for spin, and I=\frac{1}{2}
for nuclear angular momentum, which I want to add using the Clebsch-Gordon basis, so the conversion looks like:
$$
\begin{align}
\lvert 1,1\rangle &= \lvert\bigl(\tfrac{1}{2}\tfrac{1}{2}\bigr)\tfrac{1}{2}\tfrac{1}{2}...
Thank you so much for your answer. There's something weird happening when I do this calculation that I don't understand.
Now we are adding I and S, and this addition is supposed to be commutative, right? Look at the expectation value that you wrote there:
\left\langle 1 0 \frac{1}{2}...
Thank you for your reply.
The problem is exactly the way you understood it. Actually my problem is how to create the Hamiltonian matrix in the \left| {{I^2}{I_z}{S^2}{S_z}} \right\rangle basis. Can you please explain how to create that hamiltonian?
I'm trying to understand how Hamiltonian matrices are built for optical applications. In the excerpts below, from the book "Optically polarized atoms: understanding light-atom interaction", what I don't understand is: Why are the \mu B parts not diagonal? If the Hamiltonian is \vec{\mu} \cdot...
Hello guys,
I'm trying to find the configuration of two circular coils in a configuration similar to Helmholtz coils that would homogenize the magnetic field best at a volume between them.
So the first thing step I took in that is use the Biot-Savart law to calculate the magnetic field...
I'm not an expert (as you see here in my discussion), but I'd like to contribute to this. I've just read this website explaining the Quantum Eraser in detail
http://grad.physics.sunysb.edu/~amarch/ [Broken]
And I got convinced that the experiment proves that the setup of the experiment is...
Thank you for your response. Let me see if I understand this correctly. You're telling me that the states of the apparatus and the states of the system are superposed rather than being tensor-multiplied, which causes the new big system (which consists of both the apparatus and the system being...
Thanks for the answer. But why would you think that an incomplete basis should give you a unity probability, thus claiming that the Copenhagen interpretation is problematic? I mean you're simply giving your state/probability current a path to escape to a state that you haven't taken into...
I'm sorry, but I still don't see the problem. Whenever you see a state you haven't accounted for, can't you simply add it and renormalize again? Why can't this be done?
Ah, you're right. I'm sorry. That identity is obvious, I don't know why I got confused.
But doesn't this mean already that if ∥ψ′∥<∥ψ∥, then ∑|a,α><a,α| < 1, which means that the vector space isn't complete and still requires more bases, bringing us back to my cross-product example?
Thank you for your answer. I'm confused a little bit, and apparently I'm not as good as I thought in Quantum Mechanics, even after reading 3 Quantum Field Theory books and having a QFT course.
Can you please clarify, why should ∥ψ′∥≤∥ψ∥? Do the books you mentioned explain this paradigm of...
Thank you dextercioby and UltrafastPED; your comments were helpful.
vanhees71: I'm not sure how to answer your argument, but you left the main topic and went far away; maybe I'm wrong, but you probably have some problems understanding Quantum Mechanics. I'm not willing to go into a discussion...
Hello everyone,
I'm a doctoral student of particle physics in ETH Zurich, and have a question in fundamental QM.
I remember a friend telling me that the professor that taught him Quantum Mechanics in ETH Zurich did not believe in the Copenhagen interpretation, and thus taught the class...
Dear micromass, thank you for your answer and your time.
First, I would like to express my extreme disagreement with the article in the link you provided. The guy in the article is completely mixing two different things:
1- The mathematics as an entity,
2- and the way we understand...
Hello guys:
A very known fact we live is that mathematics is not falsifiable. There hasn't been a day in history when someone came up and made an experiment to prove that the equation "x^2-5x+6=0" has solutions different than 2 and 3.
In science, if we find something that doesn't comply...
Thank you all for the replies. They are all great, except the one from "Xyooj", which was hilarious.
If anyone has more to say about this, please feel free to do it :)
Hello everyone:
I'm a doctoral student in particle physics, confused about something pretty fundamental and need your help.
From what I know, the only evidence we have from the Big Bang is the Cosmic Microwave Background radiation (CMB), which showed up around 300k years after the...
Hello guys,
in the attached file, I can't understand how the guy arrived to the equation in the red rectangle.
My problem is: how could there not be dC2/dt term. Why only dC1/dt term?
ψ contains both C1 and C2, and when the derivative is applied, both have to be influenced, and both are...
Hello guys,
I'm not sure this is the right place to ask the question, but I hope someone would have experience with beam splitters cubes.
If I want to split a laser beam over more than one level with more than one beam splitter cube, so the first beam splitter splits to two beams with 50%...
Hello guys,
I need the normals of a Dodecahedron (fully symmetric 12 facets' polyhedron) given in rational numbers. I got tired searching the internet for that, so I expect something like:
{-Sqrt[1 + 2/Sqrt[5]], 0, 1/2 Sqrt[1/10 (5 - Sqrt[5])]]}
I tried Mathematica, but it gives 20 Faces for...
Thank you again for your replies.
We're doing a very specific research about Cesium magnetometers. The transitions I'm looking for are depicted in the attachment please take a look at it.
We're currently solving the Bloch's equation numerically to simulate the responce of the gas to the...
Has anyone made such a Hamiltonian and solved it? I would like to see previous contributions to this field, so that I could start working. I found nothing so far, and that's why I'm asking for help!
Well that's my question. What are the available methods for obtaining the wave-function of Cs?
I have a problem where I have a Cs gas in a chamber under a magnetic field and pumped by a laser beam. I need at least some wave function to put it in my density matrix to start doing this. But this...
I didn't find any particular thing available for the wave-function of the Cesium atom... that's why I'm surprised.
If you know any reference that would help, please let me know.
OK... let me rephrase the question...
Has anyone in the history of physics solved the Schrodinger equation of a Cesium Atom? Why can't I find anything about that?
Any references would help. Thanks!