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Under certain hypotheses on the potential energy, we prove that, for any given small value of the Planck's constant, there is an optimal truncation of the series for the approximate eigenvalues, such that the difference between an approximate and actual eigenvalue is smaller than an exponentially small function of the Planck's constant. We also prove the analogous results concerning the eigenfunctions."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Ph. 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Under certain hypotheses on the potential energy, we prove that, for any given small value of the Planck's constant, there is an optimal truncation of the series for the approximate eigenvalues, such that the difference between an approximate and actual eigenvalue is smaller than an exponentially small function of the Planck's constant. We also prove the analogous results concerning the eigenfunctions."],"dc:description.degree":["Ph. D."],"dc:identifier.other":["etd-12132002-163620"],"dc:identifier.uri":["http://hdl.handle.net/10919/30072"],"dc:publisher":["Virginia Tech"],"dc:rights":["In Copyright"],"dc:rights.uri":["http://rightsstatements.org/vocab/InC/1.0/"],"dc:subject":["exponentially accurate asymptotics"],"dc:title":["Exponentially Accurate Error Estimates of Quasiclassical Eigenvalues"],"dc:type":["Dissertation"],"thesis:degree_discipline":["Physics"],"thesis:degree_level":["doctoral"],"thesis:degree_name":["Ph. 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