= Two-site Bose-Hubbard model
{title2=$H=-t(a_L^\dagger a_R+a_R^\dagger a_L)+\tfrac U2\sum_{j=L,R}n_j(n_j-1)$}
Two localized <orbitals> coupled by <quantum tunnelling> and on-site interactions give the smallest <Bose-Hubbard model>. A symmetric <double-well potential> with lowest one-particle <energies> $E_0,E_1$ has $t=(E_1-E_0)/2$ and common diagonal <energy> $(E_0+E_1)/2$. At fixed total <particle number>, that common diagonal term is constant. A <fixed-number two-mode condensate> gives a simple <variational method> for this model, while stronger interactions can require occupation-correlated trial <quantum states>.
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