On the diagonalization of quadratic Hamiltonians
Quantum Physics
2022-01-05 v1 Other Condensed Matter
Abstract
A new procedure to diagonalize quadratic Hamiltonians is introduced. We show that one can find a unitary transformation such that the transformed quadratic Hamiltonian is diagonal but still written in terms of the original position and momentum observables. We give a general method to diagonalize an arbitrary quadratic Hamiltonian and derive a few of the simplest special cases in detail.
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Cite
@article{arxiv.2109.11864,
title = {On the diagonalization of quadratic Hamiltonians},
author = {Ville J. Härkönen and Ivan A. Gonoskov},
journal= {arXiv preprint arXiv:2109.11864},
year = {2022}
}
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7 pages