For a one-dimensional particle in an incommensurate two-period potential, projecting eigenstates of a periodic two-dimensional 'super Hamiltonian' onto the line x=y gives eigenstates of the original Hamiltonian, along with exact Green's functions and a numerical localization transition estimate.
Elser, Acta Crystallogr
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Super Hamiltonian in superspace for incommensurate superlattices and quasicrystals
For a one-dimensional particle in an incommensurate two-period potential, projecting eigenstates of a periodic two-dimensional 'super Hamiltonian' onto the line x=y gives eigenstates of the original Hamiltonian, along with exact Green's functions and a numerical localization transition estimate.