Mapping between Hamiltonians with attractive and repulsive potentials on a lattice
Mapping between Hamiltonians with attractive and repulsive potentials on a lattice
Through a simple and exact analytical derivation, we show that for a particle on a lattice, there is a one-to-one correspondence between the spectra in the presence of an attractive potential $\hat{V}$ and its repulsive counterpart $-\hat{V}$. For a Hermitian potential, this result implies that the number of localized states …