Existence and uniqueness of bound‐state eigenvectors for some channel coupling Hamiltonians

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1983
Authors
Evans, James
Evans, James
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Ames Laboratory
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Physics and Astronomy
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Mathematics
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Ames LaboratoryPhysics and AstronomyMathematics
Abstract

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.

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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.

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