Recent content by dumpling

What is the exact reasoning, that for example in the case of the radial wavefunction of hydrogen atom, we do not use singular solutions as basis, when some of those would be elements of the rigged hilbert-space?

I know that, that is the whole idea behind allowing basis to be in the rigged Hilbert-space, is it not?

Very often in standard QM books, certain states, like exponentially growing ones are rejected on the basis that they are not in L^2 space. On the other hand, scattered states are also not in L^2 spaces. This dichotomy can be repelled by using Rigged Hilbert spaces, and allowing tempered...

If you wish to derive quantum theory as Schrödinger did, there is really only two fundamental assumptions ( with the addition that you would need to derive S-equations for each class of Hamiltonian). 1) Quantum theory is not classical, that is, the Hamilton-Jacobi equation is not true. A...

I do know that supposedly the time-evolution operator is unitary. At the same time, I have come across a peculiar case during a calculation. Suppose that I have a basis that is complete (and not overcomplete), and element of Hilbert-space at t=0. For some reason, the solution of the...

My question still stands of course. But then again, if the velocity of the atom, and the energies are small, and the atom does not have spin, then isn't the only relativistic component that is relevant, is the quantization of electromagnetic field?

I thought I understood it, but I guess it is always useful to revise. I understand for example what is written here: https://farside.ph.utexas.edu/teaching/qm/lectures/node96.html Of course, actually calculating the dynamics of two interacting electrons is something i have never done, but I...

Hi! I would like to wrap my head around a relatively simple issue. Lets say that you have an excited atom, which rests in your refernce frame. When it emits light, the atom will have a backreaction, and it will "gain momentum" with the opposite direction as the photon. Of course, without...