Geodesic
Induced potential and Klauder phenomenon for even confinement potentials with singularity $\lambda x^{-2}$
Teoretičeskaâ i matematičeskaâ fizika, Tome 68 (1986) no. 1, pp. 45-57

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For the example of a one-dimensional oscillator with singular perturbation the occurrence of the strongly singular potential $A(\lambda)\delta(x)|x|^{-1}$ induced by this perturbation is investigated. The appearance of such a potential can be regarded as a generalization of the Klauder phenomenon ($A=\operatorname{const}$). The existence of induced potentials leads to two physically acceptable sets of even states of a perturbed oscillator, but only one of these goes over continuously into the set of even states of the harmonic oscillator when the perturbation is switched off. 
@article{TMF_1986_68_1_a3,
     author = {V. B. Gostev and V. S. Mineev and A. R. Frenkin},
     title = {Induced potential and {Klauder} phenomenon for even confinement potentials with singularity $\lambda x^{-2}$},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {45--57},
     publisher = {mathdoc},
     volume = {68},
     number = {1},
     year = {1986},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1986_68_1_a3/}
}
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V. B. Gostev; V. S. Mineev; A. R. Frenkin. Induced potential and Klauder phenomenon for even confinement potentials with singularity $\lambda x^{-2}$. Teoretičeskaâ i matematičeskaâ fizika, Tome 68 (1986) no. 1, pp. 45-57. http://geodesic.mathdoc.fr/item/TMF_1986_68_1_a3/