Recent content by Garlic

I'm trying to understand how exactly we calculate the detection rate in this specific multiple Stern-Gerlach setup. As written on the image, an (unpolarized) atomic beam is sent through a three Stern-Gerlach apparatuses, and the detector supposedly clicks 25% of the time. When I try to...

After struggling with this problem I finally understood it. My solution: $$ \vec{ \nabla } \cdot ( \vec{ B } \times \vec{ r } ) = \partial_i \; \epsilon_{ijk} \; B_j \; r_k $$ $$ = \epsilon_{ijk} \; ( \; ( \partial_i \; B_j \; ) r_k + B_j \; ( \partial_i \; r_k ) + B_j \; r_k \; \partial_i ) $$...

Thank you very much for your replies! Although I think I understood what you have written, now I'm stuck proving a more complex expression: ## \vec{p} \cdot \vec{A} ## where the identity ## \vec{A} = \frac{1}{2} ( \vec{r} \times \vec{B} ) ## is inserted. I am trying to prove that : $$ \vec{p}...

Dear PF, so we know that cross product of two vectors can be permutated like this: ## \vec{ \alpha } \times \vec{ \beta }=-\vec{ \alpha} \times \vec{ \beta} ## But in a specific case, like ## \vec{p} \times \vec{A} = \frac{ \hbar }{ i } \vec{ \nabla } \times \vec{A} ## the cyclic permutation of...

I understand it! I can't believe I did it! I feel intelligent :cool: Thank you so much for helping me!

So I just figured it out. :) Although the indices are upside down, but I have a feeling they are the same as in the solution. Now I'm stuck at the second part: what am I doing wrong here? Am I using a wrong lorentz matrix?

Maybe like this? $$ M' = \bar{\psi} \: (x) S(\Lambda^{-1}) \Gamma^{T}_{12} S(\Lambda) \psi \: (x) $$

I suppose: $$ A'_{\alpha \beta}= \Lambda_{\alpha}^{\: \mu} \Lambda_{\beta}^{\: \nu} A'_{\mu \nu} = \Lambda_{ \alpha}^{\: \mu} \Lambda_{\beta}^{\: \nu} \bar{\psi} \Gamma^{T}_{\mu \nu} \psi $$ So M should transform like this: $$ M_{\alpha \beta} \rightarrow M'_{\alpha \beta}= \Lambda_{\alpha}^{\...

Dear reader, there is a physics problem where I couldn't understand what the solutions. It is about the lorentz transformation of a bilinear spinor matrix element thing. So the blue colored equation signs are the parts which I couldn't figure out how. There must be some steps in between which...

Dear PF, I hope I've formulated my question understandable enough. Thank you for your time, Garli

Thank you for your quick replies :) I have found a link where it says that the associated time evolution unitary operator ## U(t,0) ## is similar to the operator ## R_n(α) ## which rotates a vector by an angle α around the axis defined by the vector ## \bar{n} ##. I diddn't understand how a...

Dear PF, As an excercise I am to find out how the expectation value of the spin operator evolves over time. There was a hint, stating that it is enough to show that $$ e^{i \frac{\phi ( \hat{n} \cdot \sigma )}{2}} \sigma_i e^{- i \frac{\phi ( \hat{n} \cdot \sigma )}{2}} = [R_{ \hat{n} }]_{ij}...

Thank you for your replies :) As I previewed my equations, they diddn't appear as Latex formulas, so I thought I got the syntax wrong and gave up :) So today I've looked at the MIT text for a few hours and tried to understand every step of it. It was certainly very interesting. I am surprised...

Dear PF community, I am back with a question :) The solutions for the quantum harmonic oscillator can be found by solving the Schrödinger's equation with: Hψ = -hbar/2m d²/dx² ψ + ½mω²x² ψ = Eψ Solving the differential equation with ψ=C exp(-αx²/2) gives: -hbar/2m (-α + α²x²)ψ + ½mω²x²ψ = Eψ...

I mean in our laboratory classes for second semester physics major students, it is something unusual that someone uses a pH Meter. He told that the pH Meter that litup suggested is being sold already calibrated, so I wouldn't have to calibrate it before using it, but once something happens it is...