Existence and uniqueness of bound‐state eigenvectors for some channel coupling Hamiltonians
For the three‐particle, two‐cluster, 2×2 channel coupling Hamiltonians used, e.g., in H+2 and He bound‐state calculations, we demonstrate that typically there exist unique eigenvectors for all bound states. This result also holds, with some technical assumptions on the potentials, for the corresponding 3×3 case provided there are no spurious eigenvectors with bound‐state eigenvalues. The proofs use the analogous results for the corresponding Faddeev‐type Hamiltonians together with spurious multiplier relationships.
This article is published as Evans, J. W. "Existence and uniqueness of bound‐state eigenvectors for some channel coupling Hamiltonians." Journal of Mathematical Physics 24, no. 5 (1983): 1160-1162, doi:10.1063/1.525845. Posted with permission.