On the diagonalization of quadratic Hamiltonians
arXiv:2109.11864 · doi:10.1088/1751-8121/ac3da5
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.
7 pages
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