Tagged Questions

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Representation of Hamiltonian in terms of “creation” and “destruction” operators

Let's have Schrodinger equation or Dirac equation in Schrodinger form: $$i \partial_{0}\Psi = \hat {H}\Psi .$$ Sometimes we can introduce some operators $\hat {A}, \hat {B}$ (the second is not ...
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Non-Hermiticity when Fourier transforming onto a finite lattice

I'm doing numerical simulations. I have the Haldane model in a honeycomb lattice where $$H = \sum \limits_{<ij>}a^\dagger_i b_j + h.c$$ Where $i$ belongs to sublattice $A$, and $j$ to ...
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The Hermiticity of the Laplacian (and other operators)

Is the Laplacian operator, $\nabla^{2}$, a Hermitian operator? Alternatively: is the matrix representation of the Laplacian Hermitian? i.e. \langle \nabla^{2} x | y \rangle = \langle x | ...
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The notion of bounded states in quantum mechanics and their characterization with operators

Is there any case of potential $V$, such that the continuity of the operator $H=c\ \Delta+V$ is not spoiled? And I don't know any non-differnetial operator examples for continous spectra. I ...
I know how to calculate the expectation of < $\Psi$|A|$\Psi$ > where the operator A is the eigenfunction of energy, momentum or position, but I'm not sure how to perform this for a pure frequency. ...