Perturbation expansions for a class of singular potentials
Copyright policy )Perturbation expansions for a class of singular potentials
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.
- Concordia University Canada
- University of Prince Edward Island Canada
81Q05; 81Q20, 81Q20, Perturbation theories for operators and differential equations in quantum theory, FOS: Physical sciences, Mathematical Physics (math-ph), Mathematical Physics, 81Q05
81Q05; 81Q20, 81Q20, Perturbation theories for operators and differential equations in quantum theory, FOS: Physical sciences, Mathematical Physics (math-ph), Mathematical Physics, 81Q05
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