Virial Theorem and Elliptic Eigenvalue Calculations on $R^N $

      The Virial Theorem is a fundamental property of multiparticle systems in quantum mechanics, and offers an elegant relationship between kinetic and potential energies of quantum states. In this talk, we present two numerical schemes based upon the Virial Theorem, the virial steepest descent and 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 schemes is presented. Concrete examples are also included and discussed.