Siegert resonance state

The Siegert resonance state provides a method of calculating the lifetime and position of the decaying state without the need to solve the TDSE. Aside from the practical advantage, they also greatly facilitate the understanding... 

O.I. Tolstikhin, V.N. Ostrovsky, H. Nakamura, Siegert pseudo-states as a universal tool Resonances, S matrix, Green function, Phys. Rev. Lett. 79 (1997) 2026. 

Here we note that the QNF Hamiltonian can be interpreted as representing the activated complex. As it has been shown above, the QNF Hamiltonian has only continuous spectrum, and so there are no bound states associated with the activated complex. Physically this corresponds to the fact that the activated complex has a finite lifetime. The latter is determined by the Gamov-Siegert resonances which we discuss in detail in Section 5. 

As we have discussed in Section 2 in classical mechanics the transition state is represented by a lower dimensional invariant subsystem, the center manifold. In the quantum world, due to Heisenberg s uncertainty principle, we cannot localize quantum states entirely on the center manifold, so fhere cannot be any invariant quantum subsystem representing the transition states. Instead we expect a finite lifetime for fhe fransition state. The lifetime of fhe fransifion sfate is determined by the Gamov-Siegert resonances, whose importance in the theory of reacfion rafes has been emphasized in fhe liferafure [61, 62]. 

Eq. (A.24). The commutativities (A.56) imply that the eigenstates of Hq f product states of the one-dimensional eigenstates of I and f. As we demonstrated in Sections 4.1 and 5 the simplicity of fhe specfral properties of I and Jk upon which the QNF is built can be exploited to give an efficient procedure to compute the CRP and the Gamov-Siegert resonances associated with the equilibrium Zq. 

To uniquely associate the unusual behavior of the collision observables with the existence of a reactive resonance, it is necessary to theoretically characterize the quantum state that gives rise to the Lorentzian profile in the partial cross sections. Using the method of SQ, it is possible to extract a Siegert state wavefunction from time-dependent quantum wave packets using the Fourier relation Eq. (28). The state obtained in this way for / = 0 is shown in Figure 3.7 this state is localized in the collinear F-H-D arrangement with three quanta of excitations in the asymmetric stretch... 

Hamiltonian (114) could be solved with a prefixed precision using the Siegert method [167]. Consequently, the scaling ansatz also gives a powerful numerical tool useful for calculating critical parameters related to the bound states, resonances, and virtual states [167,172],... 

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