Method of complex coordinates: Application to the stark effect in hydrogen

Abstract

The method of complex coordinates as applied to calculation of resonance parameters for dilatation analytic operators is discussed, and numerical evidence is presented that although the Stark potential F . is not dilatation analytic, many of the results of the theory seem to hold. In particular, Stark widths and shifts for the H atom ground state in weak and strong fields are calculated in spherical coordinates using only Lz basis functions, giving results in excellent agreement with those of methods applying detailed boundary conditions in parabolic coordinates.

Resonances in the Continuum, Field-Induced Nonstationary States, and the State- and Property-Specific Treatment of the Many-Electron Problem

“…In principle, this 'rotation' reveals the full spectrum of discrete, scattering and resonance states. Reinhardt and co-workers [34][35][36][37] found via computation on…”

Unitary transformations of a family of two-dimensional anharmonic oscillators

“…We calculated the lowest resonance for the anharmonic oscillator (10) by means of the complex rotation method [18][19][20][21] using finite basis sets of eigenfunctions of H 0 of increasing dimension up to 30 2 × 30 2 and a roughly optimal rotation angle θ = 0.06π. Table 1 shows present results and those of Witwit and Killingbeck [1] for some values of λ.…”

Resolution-of-the-identity second-order Møller–Plesset perturbation theory with complex basis functions: Benchmark calculations and applications to strong-field ionization of polyacenes

“…2 This relies on the application of complex-scaling techniques to Stark resonances. [44][45][46][47][48] Molecules exposed to static electric fields do not hold bound states, but by scaling asymptotically the electronic coordinates in the molecular Hamiltonian as r → re iθ , the new eigenfunctions become L 2 integrable. A previously hidden Stark resonance can be described in terms of the new complex eigenvalue…”