Tagged Questions

Second quantization or canonical quantization in quantum field theory and many-body systems is the collective organizing and accounting of an infinity of quantum excitations and their interactions through quantum field operators.

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Fock Subspaces and Weight Vectors

This is my first time taking a physics course (I'm a mathematics major), so I'm encountering a lot of new things, which I'm kind of expected to know. In particular, how to work with Bosons. I've got ...
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How to formulate collapse in polarization subspace of a photon?

I am wondering how to describe the collapse of a photon state when it is measured in the polarization degree of freedom (say by a filter which let pass just one particular polarisation). Let the free ...
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How to calculate the eigenstate of a lattice model in the position space

Say we have a triangular lattice, inside the unit cell there are four sites(label them as a, b, c, d) with different on-site potential energy. What I want to do is find the eigenstate in the position ...
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Derive Fermion Particle Density Operator in q-space

I am reading Bernevig's Topological Insulators and Topological Superconductors. In section 3.1.1, it gives an expression for the Fourier transformation of electron density operator, which I cannot ...
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Creation operators that differ by a reciprocal lattice vector

In very general terms, if you have an infinite lattice of atoms you can describe the physics in terms of creation (and annihilation) operators $\hat{a}_{\mathbf{R}}$, that create (and annihilate) an ...
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Bogoliubov coefficients and eigenvectors

Suppose you have diagonalized Hamiltonian $H$ in second quantization using Bogoliubov transformation. If Hamiltonian is $N \times N$ matrix, the Bogoliubov transformation will have $N$ coefficients. ...
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Single-particle operator in second quantization

I am new to second quantization and I am still rather uncomfortable with the bra-ket notation. I feel like I am slowly getting the hang of it but when it comes to shifting bra's and ket's around, I ...
On page 18, before the occupation number variables for states i and j are changed $n_i \rightarrow n'_i = n_i - 1$ and $n_j \rightarrow n'_j = n_j + 1$ respectively, could we not have rewritten eq. 1....