Electronic Resource
College Park, Md.
:
American Institute of Physics (AIP)
Journal of Mathematical Physics
35 (1994), S. 6244-6269
ISSN:
1089-7658
Source:
AIP Digital Archive
Topics:
Mathematics
,
Physics
Notes:
The perturbed-ladder-operator method is applied to the solution of the perturbed eigenequation {(d2/dx2)−[m(m+1)/x2]−b2x2+V(x)+Λ}Ψ θix)=0 where V(x)=b1(1/x)2+b2(1/x)4+... is a singular perturbation. This method, which is the extension of the Schrödinger–Infeld–Hull factorization method within the perturbation scheme, provides closed form expressions of the perturbed eigenvalues and ladder functions, by means of algebraic manipulations. As an illustrative application, an analytical solution of the spiked-harmonic-oscillator eigenequation {(d2/dx2)−b2x2−(λ/x4)+E}Ψ(x)=0 is worked out up to the second order of the perturbation, by considering specifically adapted m- and λ-dependent perturbing and unperturbed potentials in order to tentatively avoid the known difficulties of convergence of the perturbation series. Closed form expressions of the λ/x4-anharmonic-oscillator energies are obtained in terms of the coupling constant λ and the quantum number v: results following from these expressions are compared with exact available values. © 1994 American Institute of Physics.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.530673
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