Variational principle for derivation of macroscopic equations

Norman Henry March

Katsuhisa Ohta

Sami H. Altoum

The aim of this research is to derive Schrödinger equation from calculus of variations (variational principle), so we use the methodology of calculus of variations. The variational principle one of great scientific significance as they provide a unified approach to various mathematical and physical problems and yield fundamental exploratory ideas.

Abraham Klein, Toshio Marumori, Tsutomu Une

The time-dependent variational principle of the Schr\"odinger equation is applied to a formally exact solution of the Schr\"odinger equation whose variational elements are operators which define a collective subspace of the many-body system under study. This generalizes the procedure employed to derive time-dependent Hartree-Fock theory. Four distinct formally exact time-independent variational principles, including several familiar forms, are derived. Application to a class of exactly soluble models, studied in the vibrational regime, illustrates the different modes of implementation of two of the principles. The general theory of large amplitude collective motion is derived. It is shown that the principles can be applied equally well, using either boson or fermion pair degrees of freedom. Some aspects of the relation to the semiclassical limit are discussed.[NUCLEAR STRUCTURE Time-dependent variational principle for collective motion. Invariance principle of Schr\"odinger equation. Generalized coherent state trial function. Exact time-independent variational principles. Variational principle for intrinsic state. Cranking variational principle. Large amplitude collective motion. Semiclassical limit.]

Giampaolo Co’

M. C. Smith-Agreda