Resolving the Laughlin Paradox

For paired Bloch electrons in a metal not subject to Pauli exclusion, the 2-electron Hamiltonian has the form\\ \\ $H=$$-\hbar ^2\over{4m_e}$$\Delta$$_c_m+(2e) U_l_a_t_t_i_c_e(r_c_m,N_c_e_l_l) +$$e^2\over{( N_c_e_l_l r_1_2)}$$-$$\hbar ^2\over{3m_e}$$\Delta$$_1_2$, \\ \\ where $r_c_m = r_1 +r_2, r_1_2 = r_1 - r_2$, and $r_1$ and $r_2$ are position vectors in configuration space, involving independent Bravais vectors $R_1$ and $R_2$ , such that $R_1 - R_2 = R_1_2$ is an independent Bravais lattice vector, and N$_c_e_l_l$ is the number of mutually shared potential wells over which the 2 electrons are coherently partitioned with entangled local density maxima. At large N$_c_e_l_l$, the magnitude of term 3 $<<$ the magnitude of term 1. When coordinate exchange symmetry is satisfied and energy minimized, term 3 cancels term 1 at $r_1_2= 0$, eliminating the singularity in the wave equation, thereby resolving Laughlin's paradox\footnote{R.B. Laughlin, ``A Different Universe'', (Basic Books, Cambridge MA, 2005) pp. 84-85.}