The hydrogen atom in an electric field: Closed-orbit theory with bifurcating orbits

Abstract

Closed-orbit theory provides a general approach to the semiclassical description of photo-absorption spectra of arbitrary atoms in external fields, the simplest of which is the hydrogen atom in an electric field. Yet, despite its apparent simplicity, a semiclassical quantization of this system by means of closed-orbit theory has not been achieved so far. It is the aim of this paper to close that gap. We first present a detailed analytic study of the closed classical orbits and their bifurcations. We then derive a simple form of the uniform semiclassical approximation for the bifurcations that is suitable for an inclusion into a closed-orbit summation. By means of a generalized version of the semiclassical quantization by harmonic inversion, we succeed in calculating high-quality semiclassical spectra for the hydrogen atom in an electric field.

References in corpus (6)

• Bifurcations of Periodic Orbits and Uniform Approximations
• Use of Harmonic Inversion Techniques in Semiclassical Quantization and Analysis of Quantum Spectra
• Uniform Approximation for Period-Quadrupling Bifurcations
• Harmonic inversion as a general method for periodic orbit quantization
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Cited by in corpus (1)

• Photoabsorption spectra of the diamagnetic hydrogen atom in the transition regime to chaos: Closed orbit theory with bifurcating orbits