An analytical proof of saturability of an optimized lower bound for N-body Hamiltonians for some mass configurations, with arbitrary N
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Date
2006-05-03
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KheirEddine Boudjemaa
Abstract
We begin by deriving explicit formulae for the energy levels of a system of N
harmonic oscillators for two special mass configurations but for arbitrary N.
Under the same conditions, we can perform analytically all the calculational
procedure leading to an optimized lower bound for the ground state energy of an
N-body system. The lower bound obtained in this way proves to be identical to
the exact result. It is the first time, to our knowledge, that an explicit analytical
proof of saturability has been worked out.