Recent content by Dyatlov

Hello. I self-studied and have a good grasp on QM, statistical mechanics and Group theory. Next step is QFT. There are several sets of video lectures on Youtube about this subject and I am asking for a recommendation (I would like a set of videos which involves the unitary IR of the Poincare...

Bad wording I guess then. Thanks for the help, anyway!

Thanks for the replies. The title mentions that I am solving the identity for Hermitian operators. I know that ##\epsilon_{ijk}A_jB_k## is a sum over j and k, with ##j,k=1,2,3##. ##(\epsilon_{ijk}A_jB_k)^\dagger=(\epsilon_{ijk}B^\dagger_kA^\dagger_j)=-(B^\dagger \times A^\dagger)_i## Therefore...

Since ##\epsilon_{ijk}## is antisymmetric then we have ##\epsilon_{ijk}A_jB_k=A_jB_k-A_kB_j## ##A_jB_k-A_kB_j=-(B_jA_k-B_kA_j)## ##(A \times B)_i=-(B \times A)_i## Since A and B are Hermitian the same equlity holds for their self-adjoint counterparts.

Homework Statement ##(\hat A \times \hat B)^*=-\hat B^* \times \hat A^*## Note that ##*## signifies the dagger symbol. Homework Equations ##(\hat A \times \hat B)=-(\hat B \times \hat A)+ \epsilon_{ijk} [a_j,b_k]## The Attempt at a Solution Using as example ##R## and ##P## operators: ##(\hat...

Maybe this will help get you started. A time-dependent magnetic field which has time-independent z component and a circularly polarized field representing a magnetic field rotating along the (x,y) plane is: ##B(t)=B_0\hat k+B_1(coswt \hat i - sin wt \hat j)## The Hamiltonian for this field is...

Hello. I am trying to prove that the uncertainty in energy for a normalized state limits the speed at which the state can become orthogonal to itself. The problem is number 2 on https://ocw.mit.edu/courses/physics/8-05-quantum-physics-ii-fall-2013/assignments/MIT8_05F13_ps6.pdf Having issues...

Hello. I would like to check my understanding of how you transform the covariant coordinates of a vector between two bases. I worked a simple example in the attached word document. Let me know what you think.

Got it, thanks a lot.

I am trying to solve this equation: d/dx[dF(x)/dx] = [c(c+1)/x^2)F(x), where c is a constant. Do I still use the characteristic equation to solve this? EDIT: Is it solvable using Dawson's integral rule?

Thanks, got it now.

Thanks for the answer, did it and got: (dF/da) (dF/du) = (dF/da) u + (dF/du) a = (dF/du) a, since a is a constant. What am I missing here?

Hello. We have the derivative of a function: d F(x)/dx. If we substitute x = au, how can I show that d F(x)/dx = (1/a) (dF/du) ?

Yes, that was where my confusion was coming from. Thanks.

Hello! Got a bit of an issue with thew two above mentioned equations about time. From the Lorentz transformation t' = [t - (vx)/c^2]/lorentz factor, we get that the time read by a moving observer for an event in the stationary observer's frame of reference will always be slower (longer) because...