Resonance states by the generalized complex variational method

Abstract

The resonance states are presented as the complex stationary solutions of generalized secular equations. The study of the analytical behaviour of the complex stationary solutions of these equations as a function of a coupling parameter λ in the hamiltonian yields the following.

1.

(1)Criteria to distinguish between the complex stationary solutions that describe the resonances and the complex solutions that may be obtained as a result of the restrictions on the basis set.

2.

(2)Criteria and a computational procedure for judging the stability of results obtained within the framework of the complex coordinate method. On this basis it is pointed out that the enhanced stability of the resonant eigenvalue when a complex basis function is added to the real basis set is due to the fact that the expectation value of the second derivative of the hamiltonian with respect to the scaling parameter can be negative while for a real basis set it is equal to the kinetic energy and therefore gives positive values only.

Additional information

Notes on contributors

Nimrod Moiseyev

Yigal Allon Foundation Fellow