2005/03/09 by F. J. Gomez, F.J. Gómez, J. Sesma
Physics and Astronomy · #Quantum Mechanics and Applications #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #quant-ph
paper · pdf · doi:10.1088/0305-4470/38/14/009
published as J. Phys. A: Math. Gen. 38 (2005) 3193-3202 · 10 pages
arxiv created 2005/03/09 · openalex publication_date 2005/03/22 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Abstract. The determination of the eigenenergies of a quantum anharmonic oscillator consists merely in finding the zeros of a function of the energy, namely the Wronskian of two solutions of the Schrödinger equation which are regular respectively at the origin and at infinity. We show in this paper how to evaluate that Wronskian exactly, except for numerical rounding errors. The procedure is illustrated by application to the gx 2 + x 2N (N a positive integer) oscillator. PACS number: 03.65.Ge Submitted to: J. Phys. A: Math. Gen. Anharmonic oscillators 2 Quantum anharmonic oscillators have been frequently used in different branches of Physics to simulate a great variety of situations and to explain multitude of phenomena. Apart from this, since the publication of the seminal papers by Bender and Wu [1] and by Simon and Dicke [2] showing the failure of the Rayleigh-Schrödinger perturbation method, they have served to test plenty of approximate methods of solution of the Schrödinger equation. Papers dealing with the most recently proposed methods [3] contain references to older ones, that we omit for brevity. It seems, however, to have