On the spectrum of a class of quantum models
Received: 31 August 2012
Accepted: 30 November 2012
The spectrum of any quantum model whose eigenvalue equation reduces to a three-term recurrence, such as a displaced harmonic oscillator, the Jaynes-Cummings model, the Rabi model, and a generalized Rabi model, can be determined as zeros of a corresponding transcendental function F(x). The latter can be analytically determined as an infinite series defined solely in terms of the recurrence coefficients.
PACS: 03.65.Ge – Solutions of wave equations: bound states / 02.30.Ik – Integrable systems / 42.50.Pq – Cavity quantum electrodynamics; micromasers
© EPLA, 2012