Browsing by Author "KheirEddine Boudjemaa"
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Item An analytical proof of saturability of an optimized lower bound for N-body Hamiltonians for some mass configurations, with arbitrary N(KheirEddine Boudjemaa, 2006-05-03) KheirEddine BoudjemaaWe 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.Item Optimized lower bounds for N-body Hamiltonians(KheirEddine Boudjemaa, 2006-05-23) KheirEddine BoudjemaaGeneralizing a method used previously for three-body, four-body and very recently for five-body systems, we derive a lower bound for the ground state energy of an N-body Hamiltonian, with arbitrary N. Because the expression of the lower bound obtained in this way depends on a number of parameters, we obtain in fact a family of lower bounds, a lower bound for each set of values of these parameters. The best of these is of course obtained by maximizing over these parameters and is correspondingly named optimized lower bound. The set of values of the parameters corresponding to the optimized lower bound satisfy a number of relations, named universal dynamical constraints, which result from the application of a dynamical principle and are independent of the particular form of the potential. For N = 3, 4, 5, they can be worked out in the most general case. For N = 6 up, they can be worked out only for particular mass configurations. Furthermore, the optimized lower bound proves to be saturated in the harmonic oscillator case.