Variation principle for probability amplitudes

David M. Bishop, Lap Ming Cheung

Leonard Eisenbud

Jean-Paul Blaizot, Georges Ripka C

K. Robert Müller

A variation principle, similar to the Delves principle, is given for the (real) wave function itself. The principle does not give a bound. The relationship between both principles is discussed. — After proper generalization a variation principle for arbitrary probability amplitudes (or generalized Fourier coefficients) is obtained.

Douglas M. Sheppard

R Phythian

The probability amplitude for the transition of a many particle system between given initial and final states in some finite time interval is considered where these states are products of single particle functions. It is pointed out that, if this amplitude is calculated by approximating the intermediate states by means of the usual time dependent Hartree theory, a spurious time dependence of the amplitude is obtained. An alternative time dependent extension of Hartree theory, more suited to this problem, is obtained by employing suitable trial functions in a variational principle for the transition amplitude. Some simple properties of the approximation are discussed.