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Coupling constant thresholds of perturbed periodic Hamiltonians

1998
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Journal of Mathematical Physics
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We consider Schrödinger operators of the form H ϭϪ⌬ϩVϩW on L 2 (R ) ͑ϭ1, 2, or 3͒ with V periodic, W short range, and a real non-negative parameter. Then the continuous spectrum of H has the typical band structure consisting of intervals, separated by gaps. In the gaps there may be discrete eigenvalues of H that are functions of the parameter . Let (a,b) be a gap and E()(a,b) an eigenvalue of H . We study the asymptotic behavior of E() as approaches a critical value 0 , called a coupling

doi:10.1063/1.532516
fatcat:ixu2w5qynbafzgc57cglzvhcve