2007/12/12 by I. V. Dobrovolska, Dobrovolska, I. V., R. S. Tutik +1
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #Nuclear physics research studies #Quantum Mechanics and Non-Hermitian Physics #Spectral Theory in Mathematical Physics #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.0712.2037
Talk given at International School-Seminar "New physics and QCD at external conditions" (Dniepropetrovsk, Ukraine, May 3-6, 2007); 11 pages; prepared for publication in Proceedings
arxiv created 2007/12/12 · openalex publication_date 2007/12/12 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The explicit semiclassical treatment of the logarithmic perturbation theory for the bound-state problem for the spherical anharmonic oscillator and the screened Coulomb potential is developed. Based upon the ℏ-expansions and suitable quantization conditions a new procedure for deriving perturbation expansions is offered. Avoiding disadvantages of the standard approach, new handy recursion formulae with the same simple form both for ground and excited states have been obtained. As examples, the perturbation expansions for the energy eigenvalues of the quartic anharmonic oscillator and the Debye potential are considered.