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arXiv · 2109.11864

On the diagonalization of quadratic Hamiltonians

Ville J. Härkönen·Ivan A. Gonoskov
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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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Ville J. Härkönen, Ivan A. Gonoskov. 2021-09-24. On the diagonalization of quadratic Hamiltonians. https://doi.org/10.1088/1751-8121%2Fac3da5

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