2003/09/30 by Nasser Saad, Richard L. Hall, Attila B. von Keviczky · 5 citations
Mathematics · Physics and Astronomy · #Class (philosophy) #Excited state #Harmonic oscillator #Mathematical functions and polynomials #Method of averaging #Perturbation (astronomy) #Perturbation theory (quantum mechanics) #Poincaré–Lindstedt method #Quantum Mechanics and Non-Hermitian Physics #Singular perturbation #Spectral Theory in Mathematical Physics #math-ph #math.MP #msc:81Q05 #msc:81Q20
paper · pdf · doi:10.1063/1.1616996
published in Journal of Mathematical Physics 44(11), 5021-5041 (American Institute of Physics) · 23 pages
arxiv created 2003/09/30 · openalex publication_date 2003/10/24 · arxiv updated 2015/06/26 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Harrell’s modified perturbation theory [Ann. Phys. (N.Y.) 105, 379 (1977)] is applied and extended to obtain nonpower perturbation expansions for a class of singular Hamiltonians H=−(d2/dx2)+x2+(A/x2)+(λ/xα) (A⩾0,α>2), known as generalized spiked harmonic oscillators. The perturbation expansions developed here are valid for small values of the coupling λ>0, and they extend the results which Harrell obtained for the spiked harmonic oscillator A=0. Formulas for the excited states are also developed.