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Zbl 0658.46063
Hall, Richard L.
The ground-state energy of a system of identical bosons. (English)
[J] J. Math. Phys. 29, No.4, 990-994 (1988). ISSN 0022-2488; ISSN 1089-7658/e

A system of N identical bosons is studied, each having mass m, which interact in ${\bbfR}\sp 3$ 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 $V\sb{ij}=\gamma \vert r\sb i-r\sb j\vert$ the bounds imply that the ground-state energy is given by ${\cal C}=C(N)(N-1)(\hslash\sp 2/m)\sp{1/3}(\gamma N/2)\sp{2/3}$, where $2.3381<C(N)<2.343 52$. The energy is therefore determined in this case with error $<0.116\%$ for all $N\ge 2$. Similar results are given for other power-law potentials.

MSC 2000:: *46N99 Appl. of functional analysis
81V25 Other elementary particle theory

Keywords: system of N identical bosons; attractive central pair potentials; nonrelativistic quantum mechanics; lower energy bound; upper energy bound; variational methods; power-law potentials

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