Method of Moments in Quantum Mechanics

Abstract

An approximation technique for quantum-mechanical problems based on the expectation values of the powers of the Hamiltonian is developed. The mathematical foundations on which this approach is based are the method of moments employed in probability theory, and the theory of orthogonal polynomials. In practice this method constitutes an extension of the Rayleigh-Ritz principle and gives a systematic method of improving the trial function.