Vol. 4, No. 3-4, 2016

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ISSN: 2325-3444 (e-only)
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Quantum mechanics: some basic techniques for some basic models, II: The techniques

Vincenzo Grecchi

Vol. 4 (2016), No. 3-4, 353–372
Abstract

This paper is a continuation of the previous one: “Quantum mechanics: some basic techniques for some basic models, I: The models”. The main subject is the perturbation theory in quantum mechanics giving diverging perturbation series for the energy levels of the oscillators. Thus, a short historical introduction on the methods of the sum of diverging power series is given.

Keywords
confinement of the nodes and exact quantization condition, Stokes lines, Stokes sectors, generalized change of representation, Riccati equation and semiclassical series, divergent perturbation series, sum of divergent series
Physics and Astronomy Classification Scheme 2010
Primary: 03.65.-w
Milestones
Received: 29 September 2016
Accepted: 31 October 2016
Published: 4 February 2017

Communicated by Francesco dell'Isola
Authors
Vincenzo Grecchi
Dipartimento di Matematica
Università di Bologna
I-40126 Bologna
Italy
Gruppo Nazionale di Fisica Matematica
Istituto Nazionale di Alta Matematica Francesco Severi
I-00185 Roma
Italy