Bound States and the Interaction Representation

Rytis Juršėnas

In a series of recent papers it was shown that, when the attractive s-wave interaction is dominant, the spin-orbit coupled fermions form a bound state. Attributed to a convenient momentum representation, it became a common condition of agreement to express the bound state as a function of the center-of-mass momentum Q. In this letter we prove that the bound state of Rashba fermions does not depend on the chosen representation. That is, all the states characterized by nonzero Q fail to obey the translation symmetry.

Takafumi Kita

S. T.

The temporal development of the state vectors in the interaction representation is investigated for a quantum-mechanical system that has bound states. It is shown that there is a non-unitary operator which determines the variation of the state vectors of the free states. This operator satisfies the same differential equation and initial condition as the unitary operator which transforms a state vector at the remote past to the state vector at a finite time or in the remote future. The present investigation is relevant to a remark made by H. S. Snyder.No iteration process is made use of in the general investigation. Born's method of successive approximations is discussed at the end.

Charles G. Wohl

Franco Antonio Gianturco, Francesco Paesani, I. Baccarelli +6 more

The weakly bound diatomic systems He24 and HeH−4 have been found able to support only one bound state for J=0, although the latter also supports an additional bound state for J=1. In the present paper we, therefore, study the structure of the bound states which might exist for the weakly bound triatomic He24H−, in its J=0 state, by describing the full potential as a simple addition of two-body (2B) interactions. We carry out bound state calculations using both Jacobi coordinates within a discrete variable representation (DVR) and pair coordinates with a distributed Gaussian function (DGF) expansion. The system is shown to possess two bound states with respect to its lower dissociation threshold and two further “ghost” states before the complete break-up threshold. The spatial structures of such states and of the floppy complex are analyzed in detail, as is the possibility of detecting Efimov-type states in such a weakly bound aggregate. Finally, the inclusion of three-body (3B) forces in the description of the full interaction and its effect on the number of possible bound states is also discussed.