Vol. 4, No. 3-4, 2016

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Quantum mechanics: some basic techniques for some basic models, I: The models

Vincenzo Grecchi

Vol. 4 (2016), No. 3-4, 335–352
DOI: 10.2140/memocs.2016.4.335

This is a short review of the main results on the oscillators considered basic models in quantum mechanics. Since the potential is polynomial, it is possible to extend the stationary states to entire functions on the complex plane where the semiclassical theory works better. The control on the energy levels is based on the isolation of the nodes, the zeros stable at the unperturbed limit. A new and simple model for the process of racemization of chiral molecules is added.

quantum oscillators, $PT$ symmetry, isospectral Hamiltonians, spectral analysis, analyticity of the eigenvalues
Physics and Astronomy Classification Scheme 2010
Primary: 03.65.-w
Received: 25 March 2016
Revised: 29 September 2016
Accepted: 31 October 2016
Published: 4 February 2017

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