Can the eigenstates of a many-body hamiltonian Be represented exactly using a general two-body cluster expansion?
Using a general two-body exponential parametrization for the wave function, the Nakatsuji two-particle density equation [Phys. Rev. A 14, 41 (1976)] is transformed into a set of nonlinear algebraic equations in which the number of unknowns precisely equals the number of equations. Since the Nakatsuji two-particle density equation is equivalent to the time-independent Schrodinger equation for Hamiltonians containing up to two-body interactions, the answer to the title question is affirmative, provided the equations have solutions. Practical implications of the parametrization and possible approximation schemes are briefly discussed.
Nooijen
M
Chemistry Department, Princeton University, Princeton, New Jersey 08544, USA.