Abstract
Several lower bounds on the ground state energy of Schrödinger operators with non-confining potentials \({V_{\alpha}(x) = {\prod_{j=1}^{n}} |x_{j}|^{\alpha_{j}}}\), \({\alpha_{j} > 0}\), on \({{\mathbb R}^{n}}\) are obtained. These results lead to explicit (computable) strictly positive lower bounds and can be generalized to certain ‘product’-potentials.
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Camus, B. Lower Bounds for Non-Classical Eigenvalue Problems. Integr. Equ. Oper. Theory 85, 25–36 (2016). https://doi.org/10.1007/s00020-015-2270-1
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DOI: https://doi.org/10.1007/s00020-015-2270-1