Formally exact quantum variational principles for collective motion based on the invariance principle of the Schrödinger equation
- 1 January 1984
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review C
- Vol. 29 (1) , 240-252
- https://doi.org/10.1103/physrevc.29.240
Abstract
The time-dependent variational principle of the Schrödinger equation is applied to a formally exact solution of the Schrödinger 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.Keywords
This publication has 29 references indexed in Scilit:
- Formally exact quantum variational principles for collective motion based on the invariance principle of the Schrödinger equationPhysics Letters B, 1982
- Self-Consistent Collective-Coordinate Method for the Large-Amplitude Nuclear Collective MotionProgress of Theoretical Physics, 1980
- Concept of a Collective Subspace Associated with the Invariance Principle of the Schrodinger Equation: A Microscopic Theory of the Large Amplitude Collective Motion of Soft NucleiProgress of Theoretical Physics, 1980
- The concept of a collective path and its range of validityNuclear Physics A, 1978
- A consistent microscopic theory of collective motion in the framework of an ATDHF approachAnnals of Physics, 1978
- The coupling of a large amplitude collective motion to RPA excitationsNuclear Physics A, 1977
- Adiabatic time-dependent Hartree-Fock theory in nuclear physicsNuclear Physics A, 1977
- A Microscopic Theory of Large Amplitude Nuclear Collective MotionProgress of Theoretical Physics, 1977
- Adiabatic and non-adiabattc cranking models for the solution of the large amplitude time-dependent Hartree-Fock equations and the calculation of nuclear energy surfacesNuclear Physics A, 1974
- Choice of the constraining operator in the constrained hartree-fock methodNuclear Physics A, 1974