Recent content by Snarky Fellow

As peteratcam has noticed, wavefunction function can be obtained as matrix element \langle 0|\hat \Psi |\psi_k \rangle . We can't get a wavefunction as the expectation in a state with defined number of particles. It's due to the fact that \hat \Psi decreases number of particles so in order to...

Yes, field operator \hat \Phi and wave function \phi are very similar objects. The formal reason is that \hat \Phi(x) = \sum_k \phi_k(x) \hat a_k - it is a "superposition" of wave functions with coefficients being annihilation operators. That's why the technique is called "second quantization"...

Well, perturbation theory is mainly not only the tool to predict small corrections. The thing is that even small changes in the hamiltonian (which are usually connected with some new physics) can result in dramatically new behaviour. Imagine that we have two quantum states with the same energy...

If we deal with an eigen-state of hamiltonian, which is static in some sense, than due to the symmetry the mean momentum will be equal to zero - you're right. Of course, we can take any superposition of eigen-states, where the symmetry could be broken by our choice, but it's out of interest in...

Well, around p=0 one needs to distinguish \Delta p and p, but in fact we are interested only in \langle p^2 \rangle that is equal to \langle\Delta p^2 \rangle in case the mean momentum is 0.