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...
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.
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?
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...