the approach I am chasing is with n = ##n_1 +\n_2 + n_3## and m = ##m_1 + m_2+m_3##
the angle between is ##\theta##
##n- = n_1 - i*n_2 and n+ = n_1 + i*n_2## likewise for m- and m+
$$\begin{pmatrix}\sqrt{ \frac{1+m_3} {2} } && \frac{1-m_3}{m+}\sqrt{\frac{1+m_3}{2}}...
I don't think we are on the same page, I am trying to see if I am close to the ##\frac{1}{2}(1-\cos(\theta))## result
I feel like I am close and don't want to give up again
From the lecture I did the inner product (squared) and worked through a lot of mess
My question is not on setting up the...
here is the link to the lecture. He (Dr. Susskind) sets up the QM eigenvectors. I am just trying to do the brute force calculation to get ##\frac{1}{2} 1+\cos(\theta))## . He says that this result can come out of "just" the algebra
(You see I must be close) Unfortunately I am 10+ pages of...
From Dr. Leonard Susskind's Stanford Lecture: Quantum Entanglement, Lecture 4, he sets up a "given particle is spin up along n (arbitrary direction) and discusses : what is probability we measure up along another arbitrary m directionHe does all of the setup, - calculates the eigenvectors and...
Hello,
Just for fun - I am trying to go through The Feynman’s Lectures: Lecture #26 – Volume 1: The Principle Of Least Time. I am stuck on Figure 26-4 and specifically showing the two angles with the “double arcs” are equal. The angle of reflection BCN’ and XCF.
Maybe I am just that rusty on...
Thank you so much!
Yep - I (now) see it after writing out a few more terms (and looking up the expansion for sin and cos), and squaring the matrix gives the unit matrix - so some terms have the original matrix while the others have the unit matrix
I see that "half" of the series gives sin and...
Hello,
I was watching a video lecture from MIT 8.04 (Allan Adams)– lecture #24 (around the 38 minute mark give or take)
The topic is quantum computing, Dr. Adams is deriving / explaining how to get various computing operations. For the “NOT” operation he explains that the operator
$$ U_{Not}...
Hello,
Within Griffith's text - chap 12 section 12.2 page 423 - this is a brief summary of Bell's Theorem and description of Bell's 1964 work.
There is a table on page 423 showing the spin of the electron and positron (from pi meson decay) - these would be in the singlet state, one would be...
crap, went too fast
(I did on scratch paper earlier the "characteristic equation" deal for finding eigenvalues - the determinant resulting from subtracting the eigenvalues times the identity matrix and setting to zero ...
there I got $$ \pm \frac{\hbar}{2} $$
I should have caught that. I knew...
shoot, (wasn't being careful) , should have looked up the actual matrix operation -
$$
\frac{1}{\sqrt{2}}\begin{pmatrix}
0&\frac{\hbar}{2}\\ \frac{\hbar}{2}&0\end{pmatrix} \begin{pmatrix}
1\\-1\end{pmatrix} = \lambda \frac{1}{\sqrt{2}}\begin{bmatrix} 1 \\ -1 \end{bmatrix}
$$
2 equations...
well, at the risk of showing that I do not understand ...
either lone state $$
\begin{pmatrix}
1\\0\end{pmatrix} or
\begin{pmatrix}
0\\1 \end{pmatrix}
$$
would work but that would not be a superposition
and the boring matrix$$
\begin{pmatrix}
0\\0\end{pmatrix}
$$ giving 0=0
is not a state...
ok,
I think I'm getting it (I was going to say I have it but realized I should not go that far , because you all have seen my struggle)
Below is my explanation to check and see if I have it ( I do agree that the explanation has been within the tread all along) Also for what it's worth the...
I am not with you, what are you telling me here? I can duplicate that and I see the result within the text,
I am trying to chase what PeterDonis said : "the state he ends up with by forming the superposition is an eigenState of Sx")
I solved for the eigenstates of Sx but don't know where to...