Operator method for solution of the Schrödinger equation with the rational potential

Abstract

The eigenvalue problem for one-dimensional Schrödinger equation with the rational potential is numerically solved by the operator method. We show that the operator method, applied for solving the Schrödinger equation with the nonpolynomial structure of the Hamiltonian, becomes more efficient if a nonunitary transformation of the Hamiltonian is used. We demonstrate on numerous examples that this method can handle both perturbative and nonperturbative regimes with very high accuracy and moderate computational cost.