Exponentially Accurate Error Estimates of Quasiclassical Eigenvalues
Toloza, Julio Hugo
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We study the behavior of truncated Rayleigh-SchrÃ¶odinger series for the low-lying eigenvalues of the time-independent SchrÃ¶odinger equation, when the Planck's constant is considered in the semiclassical limit. 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.
- Doctoral Dissertations