Real stabilization of resonance states employing two parameters: basis set size and coordinate scaling

Abstract

The resonance states of one- and two-particle Hamiltonians are studied using variational expansions with real basis-set functions. The resonance energies, $E_r$, and widths, $\Gamma$, are calculated using the density of states and an ${\mathcal{L}}^2$ golden rule-like formula. We present a recipe to select adequately some solutions of the variational problem. The set of approximate energies obtained shows a very regular behaviour with the basis-set size, $N$. Indeed, these particular variational eigenvalues show a quite simple scaling behaviour and convergence when $N\to \infty$. Following the same prescription to choose particular solutions of the variational problem we obtain a set of approximate widths. Using the scaling function that characterizes the behaviour of the approximate energies as a guide, it is possible to find a very good approximation to the actual value of the resonance width.

21 pages, 7 figures (accepted for publication in Journal of Physics B.)

References in corpus (2)

• Entropy, fidelity, and double orthogonality for resonance states in two-electron quantum dots
• The scaling of the density of states in systems with resonance states

Cited by in corpus (2)

• Excited-State Trions in Two Dimensional Materials
• Two-electron resonances in quasi-one dimensional quantum dots with Gaussian confinement