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The ground-state energy of a system of identical bosons. (English) Zbl 0658.46063
A system of N identical bosons is studied, each having mass m, which interact in 3 via attractive central pair potentials and obey nonrelativistic quantum mechanics. A lower energy bound is found by the equivalent two-body method. An upper energy bound established previously on the basis of field theory is now derived by variational methods within conventional quantum mechanics. In the case of the linear potential V ij =γ|r i -r j | the bounds imply that the ground-state energy is given by 𝒞=C(N)(N-1)( 2 /m) 1/3 (γN/2) 2/3 , where 2·3381<C(N)<2·34352. The energy is therefore determined in this case with error <0·116% for all N2. Similar results are given for other power-law potentials.
MSC:
46N99Miscellaneous applications functional analysis
81V25Other elementary particle theory