= Two-mode approximation for a Bose gas
{title2=$\hat\psi(\mathbf r)\simeq\varphi_L(\mathbf r)a_L+\varphi_R(\mathbf r)a_R$}
Project a <quantized field> onto two low-<energy> <orbitals>. A sufficient regime has <temperature>, hopping and interaction shifts small compared with the <energy gap> to discarded <orbitals>. Small interwell <contact interaction> integrals can then be neglected while retaining a small <quantum tunnelling> matrix element. The projected field's <operator commutator> is the two-mode <projection operator> kernel, rather than a complete spatial <Dirac delta function>.
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