Recent content by Rayan

I'm trying to understand how quantum systems behave when they are perturbed, and I'm using the quantum harmonic oscillator as a model. I start by implementing a symmetric gaussian shaped bump in the middle of the harmonic oscillator, and then i propagate the wave functions in time. the...

So first I derived the expressions for the dynamics of the spin operators and got: $$ \frac{d\hat{S}_y}{dt} = w\hat{S}_x^H $$ $$ \frac{d\hat{S}_x}{dt} = w\hat{S}_y^H $$ $$ \frac{d\hat{S}_z}{dt} = 0 $$ Now I want to calculate the time-dependence of the expectation values of the spin operators...

So I have the solution here and trying to understand what happened at the beginning of the second row! How did we get the exponential $$e^{i(\omega_m - \omega_0 ) t' }$$ ?

If we for example have such a bipartite state: $$ | \phi > = \frac{1}{2} [ |0>|0> + |1>|0> + |0>|1> + |1>|1> ] $$ What is the easiest way to compute a density matrix of bipartite states? Should I just compute it as it is? i.e: $$ \rho = | \phi > < \phi | $$ Or should I convert to matrix form...

You're right! I just updated my question with the steps!:)

So first I rewrote H as a matrix: $$ H = \begin{pmatrix} a & b \\ b & c \end{pmatrix} $$ And tried to find the eigenvalues/energies of H, so I solved $$ det (H - \lambda I ) = \begin{vmatrix} a-\lambda & b \\ b & c-\lambda \end{vmatrix} = (a-\lambda)(c-\lambda) - b^2 = ac - a\lambda -...

So I thought that when the $m_l = 1$ beam passes through the second SG-magnet, it should split into 3 different beams with equal probability corresponding to $ m_l = -1 , 0 , 1 $ since the field here is aligned along z-axis and hence independent of the x-axis splitting. And I thought that the...

Bohr magneton

The intensity of the transitions? But It does not really help me to know which peaks corresponds to the transition I'm looking for

I suppose that the peaks can be used to get a difference in the wave number for the transition, and from that I can get the energy difference! Am I thinking right here?

But I don't really know how I am supposed to find the energy difference from the graph, how can I know which peaks to use?

I tried to show this equality by explicitly determining what $$ \overline{(\Delta \eta)^2} $$ is, but I got a totally different answer for some reason, here is my attempt to solve it, what did I miss?

What happens generally when a neutrino/anti-neutrino collides with a light vs heavy atom? My guess is, since neutrinos have very low cross section, their interaction is weak and therefore it will be an elastic scattering! For example: $$ \overline{\nu} + He^3 \rightarrow \overline{\nu} + He^3...

You're totally right! I managed to solve this integral instead and got the right answer! Thank you so much!!:)

So my first thought was that I can just use Fourier trick and integrate: $$ F(q^2) = \int_V \rho(r) \cdot e^{ i \frac{ \vec{q} \cdot \vec{r} }{h} } d^3r $$ $$ F(q^2) = 2\pi \rho_0 \int_0^{\infty} r^2 \cdot e^\frac{-r}{R} dr \cdot \int_0^{\pi} \sin{\theta} \cdot e^{ -i \frac{q \cdot r...