Convexity Properties of Coulomb Systems
Usually when one calculates the eigenvalues Ej(α) of a Hamiltonian H = HO + αV, Ej(O) being known, one attempts a Taylor expansion: Ej(α) = Ej(O) + α Ej!(O)+... Unfortunately, even when this series converges, there is no garanty that the first few terms will be close to Ej(α). For instance, if Ej(α) is a rapidly oscillating function, a linear or parabolic approximation will evidently not be very good. However, for the ground state this cannot happen because of the
KeywordsGround State Energy Concave Function Essential Spectrum Schrodinger Equation Convexity Property
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