Functional integration, Padé approximants, and the Schrödinger equation Available to Purchase

A method for finding the eigenvalues and the eigenvectors of the Schrödinger Schrödinger equation is presented. If H = T + V is an M−body Hamiltonian, we use Trotter’s formula in the form e^−βT/n e^−βV/n ∼ e^−βH/n (for n large). This allows the computation of the matrix elements of e^−βH in the configuration representation, and the moments μ_r = (ψ,(e^−βH)^rψ) (r=1,2,⋅⋅⋅) for any wavefunction ψ. From the moments μ_r we compute the [N − 1/N] Padé approximant, whose poles are the approximate eigenvalues of e^−βH. The convergence of the method is proved and asymptotic formulas for the matrix elements of e^−βT projected on states of given angular momentum are derived.