Application of the virial theorem for improving eigenvalue calculations of multiparticle systems

The virial theorem is a fundamental property for multiparticle systems in quantum mechanics, and offers an elegant relationship between kinetic and potential energies of quantum states. In this paper, we study applications of the virial theorem for improving eigenvalue calculations of multiparticle systems. We propose the virial steepest descent scheme and the two-point linear extrapolation, to improve the accuracy of such eigenvalue calculations through post-processing eigenvalue data obtained from standard methods. Mathematical analysis of both methods is presented. Examples are included to illustrate the efficiency of both methods.