= Thomas–Fermi profiles for unequal condensate trap curvatures
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{title2=$n_1=\frac{U_{22}(\mu_1-A_1r^2)-U_{12}(\mu_2-A_2r^2)}D$}
For a miscible <two-component Bose-Einstein condensate> with $V_i=A_ir^2$, $D=U_{11}U_{22}-U_{12}^2>0$, invert the local interaction matrix. The displayed result and $n_2=[U_{11}(\mu_2-A_2r^2)-U_{12}(\mu_1-A_1r^2)]/D$ hold in the overlap region. Factoring by $R_i^2=\mu_i/A_i$ puts the ratio $\lambda=A_2/A_1$ in the first profile and $\lambda^{-1}$ in the second. Outside overlap, a negative formal density must be replaced by the appropriate single-component solution, not retained as a physical density.
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