Rapidly Convergent Lower Bounds for the Schrödinger-Equation Ground-State Energy

We present a new and fundamental approach for generating rapidly convergent lower and upper bounds to the ground-state energy of a bosonic system, $E_g$. The bosonic ground-state wave function defines a moments problem because it both is nonnegative and exhibits rapid asymptotic decrease. Through the use of the Hankel-Hadamard determinant inequalities associated with this moments problem one can constrain $E_g$ through exponentially convergent bounds. Extensions to excited bosonic states and fermionic systems are briefly outlined.