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Moment based methods have produced efficient multiscale quantizationalgorithms for solving singular perturbation/strong coupling problems. One ofthese, the Eigenvalue Moment Method (EMM), developed by Handy et al (Phys. Rev.Lett.{\bf 55}, 931 (1985); ibid, {\bf 60}, 253 (1988b)), generates converginglower and upper bounds to a specific discrete state energy, once the signatureproperty of the associated wavefunction is known. This method is particularlyeffective for multidimensional, bosonic ground state problems, since thecorresponding wavefunction must be of uniform signature, and can be taken to bepositive. Despite this, the vast majority of problems studied have been onunbounded domains. The important problem of an electron in an infinite quantumlens potential defines a challenging extension of EMM to systems defined on acompact domain. We investigate this here, and introduce novel modifications tothe conventional EMM formalism that facilitate its adaptability to the requiredboundary conditions.Comment: Submitted to J. Phys.

Generating bounds for the discrete state energy values of the infinite quantum lens potential