Recent content by Sparky_

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...

hmm, multiplying Sx and the above I get 0 $$ \begin{pmatrix} 0&1\\1&0\end{pmatrix} \begin{pmatrix} 1\\-1\end{pmatrix}\\ = 0-1+1+0 $$

wait . how about $$ | \psi \rangle = \frac{1}{\sqrt{2}} ( \begin{pmatrix} 1\\0\end{pmatrix} - \begin{pmatrix} 0\\1 \end{pmatrix} )\\ | \psi \rangle = \frac{1}{\sqrt{2}} \begin{pmatrix} 1\\-1\end{pmatrix} $$

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...