Binding energies of semirelativistic N-boson systems

Details Binding energies of semirelativistic N-boson systems Binding energies of semirelativistic N-boson systems

2007-04-26

arxiv.org/abs/0704.3580v1

J.Phys.A40:6183-6192,2007

Physics

Mathematical Physics

11 pages

Scientific paper

10.1088/1751-8113/40/23/012

General analytic energy bounds are derived for N-boson systems governed by semirelativistic Hamiltonians of the form H=\sum_{i=1}^N \sqrt(p_i^2+m^2) + \sum_{1=i \ge generally, and we prove this for N=3, and for N=4 when m=0. The conjecture is also valid generally for the harmonic oscillator and in the nonrelativistic large-m limit. This formulation allows reductions to scaled 3- or 4-body problems, whose spectral bottoms provide energy lower bounds. The example of the ultrarelativistic linear potential is studied in detail and explicit upper- and lower-bound formulas are derived and compared with earlier bounds.

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