Dr Candadi V Sukumar

Abstract:

In variational solutions of differential or integral equations the variance integral and variance sum provide measures of the inadequacy of the trial function. For certain potential-scattering problems the variance integral can be used to derive rigorous upper and lower bounds to the phase shift. In more general scattering problems, the study of the variance sum or integral gives a check on the convergence of the standard variational calculations, and an alternative criterion for choosing the best trial function. Results are shown for an attractive exponential potential. © 1972 The American Physical Society.

Abstract:

Generalisations of the virial theorm in Classical Mechanics and Quantum Mechanics are examined. It is shown that the generalised virial theorem in Quantum Mechanics leads to certain relations between matrix elements. The differences between the generalisations in Classical and Quantum Mechanics are identified. Some results arising from the radial Schrodinger equation in Quantum Mechanics are discussed. It is also shown that the generalisations of the virial theorem may be extended to arbitrary number of dimensions.