three-body

generator coordinate

Physical review

Here, we explore variational approach to the finite-volume &lt;math display='inline'&gt;&lt;mrow&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;/mrow&gt;&lt;/math&gt;-body problem. The general formalism for &lt;math display='inline'&gt;&lt;mrow&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;/mrow&gt;&lt;/math&gt; non-relativistic spinless particles interacting with periodic pair-wise potentials yields &lt;math display='inline'&gt;&lt;mrow&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;/mrow&gt;&lt;/math&gt;-body secular equations. The solutions depend on the infinite-volume &lt;math display='inline'&gt;&lt;mrow&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;/mrow&gt;&lt;/math&gt;-body wave functions. Given that the infinite-volume &lt;math display='inline'&gt;&lt;mrow&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;/mrow&gt;&lt;/math&gt;-body dynamics may be solved by the standard Faddeev approach, the variational &lt;math display='inline'&gt;&lt;mrow&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;/mrow&gt;&lt;/math&gt;-body formalism can provide a convenient numerical framework for finding discrete energy spectra in periodic lattice structures.

Variational approach to N -body interactions in finite volume