A Possible Extension of a Trial State in the TDHF Theory with a Canonical Form to the Lipkin Model: -- Canonicity Conditions and Dynamical Treatment of Classical and Quantal Variables in an Extended State of the su(2)-Coherent State --
Y. Tsue, H. Akaike · Progress of Theoretical Physics · 2005
With the aim of extending the TDHF theory in canonical form to the Lipkin model, the trial state for the variation is constructed. This state is an extension of the Slater determinant. The canonicity condition is imposed to formulate the variational approach in canonical form. A possible solution of the canonicity condition is given, and the zero-point fluctuation induced by the uncertainty principle is investigated in terms of the minimum uncertainty relation, which leads to a better approximation of the ground state energy. Further, the time evolution of both sets of canonical variables, which represent the classical motion and quantal effects, is examined.