Upper Bounds to Eigenvalues of the One-Dimensional Sturm-Liouville Equation

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Abstract
This work develops a straightforward technique for giving an upper bound to any eigenvalue of the one dimensional Sturm‐Liouville problem. It is shown that any trial function that fulfills the proper boundary condition of the problem and possesses the same number of nodes as an exact eigenfunction of the problem can provide an upper bound to that eigenfunction's eigenvalue. Application of the above technique is made to provide a one‐sided bound to quantum mechanical scattering phase shifts.

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