Second quantization Definition and 63 Threads

Hi guys Today my lecturer talked about second quantization, and at the end he talked about free fermions in second quantization. He said that free electrons in second quantization satisfy that their Hamiltonian is only written as a linear combination in terms of c^\dagger c (the creation and...

Hi all I am reading about second quantization. The kinetic energy operator T we write as \hat T = \sum\limits_{i,j} {\left\langle i \right|T\left| j \right\rangle } \,c_i^\dag c_j^{}. Now, the creation and annihilation operators really seem to be analogous (in some sense) to the...

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...

Hi. In second quantization (not QFT or anything advanced like that) we have the particle density \hat n(x)=\Psi^{\dagger}(x)\Psi(x) using the usual field creation/annihilation operators. For a single particle we obtain for the expectation value in the state |\psi\rangle: \langle \psi |...

In coordinate representation in QM probality density is: \rho(\vec{r})=\psi^*(\vec{r})\psi(\vec{r}) in RSQ representation operator of density of particles is \hat{n}(\vec{r})=\hat{\psi}^{\dagger}(\vec{r})\hat{\psi}(\vec{r}) Is this some relation between this operator and density...

Homework Statement (from "Advanced Quantum Mechanics", by Franz Schwabl) Show, by verifying the relation \[n(\bold{x})|\phi\rangle = \delta(\bold{x}-\bold{x'})|\phi\rangle\], that the state \[|\phi\rangle = \psi^\dagger(\bold{x'})|0\rangle\] (\[|0\rangle =\]vacuum state) describes a...

Hi! Is there a common way to write a fermionic Fock space (finite dimensional) as a tensor product such that it is possible to do a partial trace over one particle type? Sorry, if this is an obvious question, but I just can't see it. Thanks!

I am searching material in second quantization in ashtekar-like formulation gravity. Somebody knows something like that? thanks

So I actually decided to make an effort to study for my quantum final ahead of time, and I'm trying to find books that cover second quantization. If possible I'd like to find a book that gives a decent explanation (with examples, maybe?) of the Bogoliubov transformation. Does anyone have any...

When defining a field operator, textbooks usually say that one can define an operator which destroys (or creates) a particle at position r. What does this really mean? Are they actually referring to destroying (or creating) a state who has specific quantum numbers associated with the geometry...

Write momentum, kinetic and potential energy, and two particle interaction in second quantization. That is the question that I need to answer for my exam, but I don't have any idea what second quantization is, except that you can solve harmonic oscilator by using ladder operators. I can't find...

Why the name "Second Quantization"? Hi all, The title said it all. My question is: How is one to interpret the name second quantization ? Which specifically is quantized twice ? Best Wishes DaTario

The quantum theory of field is sometimes known as second quantization. There are two distinct types of field in physics: 1. Scalar field. 2. Vector field. For each field, a force is supposed to be associated with it. But for the scalar field, this force is zero. This zero-force...