Abstract
The stationary Schrödinger equation is ∂ 2x φ + λV(x)φ=zφ for φ∈ℒ2(R +,dx). If the potential is bounded below, singular only atx=0, negative on some compact interval and behaves likeV(x)∼1/x μ asx→∞ with 2≧μ>0, then the system admits shape resonances which continuously become eigenvalues as λ increases. Here λ>0 and for μ=2 a sufficiently large λ is required. Exponential bounds are obtained on Im(z) as λ approaches a threshold. The group velocity near threshold is also estimated.
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Communicated by B. Simon
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Pravica, D.W. Spectral resonances which become eigenvalues. Commun.Math. Phys. 182, 661–673 (1996). https://doi.org/10.1007/BF02506421
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DOI: https://doi.org/10.1007/BF02506421