Recent content by Alexios

Thanks a lot. I'm trying now to derive the second quantized expression for a general two-body operator \hat{V}. Diagonal representation: \hat{V}=\frac{1}{2}\sum_{ij} v_{ij}\hat{P}_{ij} where \hat{P}_{ij} = a_i^\dagger a_j^\dagger a_j a_i counts the number of pairs of particles in states...

Thanks, that makes sense to me. As far as I know, the momentum operator in 3 dimensions should be \hat{P}=-i\hbar \int d^3 x a^\dagger (x) \nabla a(x) Your equation slightly modified gives \int \int dx_1\, dx_2\, a^\dagger (x_2)\langle x_2|\left(\sum \hat{P}_i |p_i\rangle \langle...

Hello, I'm struggling with the second quantization formalism. I'd like to derive the hamiltonian of a system with non-interacting particles \hat{H}=\int dx\,a(x)^\dagger \left[\frac{\hat{P}}{2m}+V(x)\right]a(x), where a(x) = \hat{\Psi}(x). I know the second quantized representation of a...