Geodesic
Strongly singular potentials in one-dimensional quantum mechanics
Teoretičeskaâ i matematičeskaâ fizika, Tome 41 (1979) no. 3, pp. 291-302
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The algebra of one-dimensional generalized functions constructed in the author's earlier [1] is used to develop a general method for obtaining one-dimensional Schrödinger equations with strongly singular concentrated potentials and with positive-definite metric. Examples of exact solutions to such equations are given for both reuormalizable and nonrenormalizable potentials. 
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     author = {Yu. M. Shirokov},
     title = {Strongly singular potentials in one-dimensional quantum mechanics},
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Yu. M. Shirokov. Strongly singular potentials in one-dimensional quantum mechanics. Teoretičeskaâ i matematičeskaâ fizika, Tome 41 (1979) no. 3, pp. 291-302. http://geodesic.mathdoc.fr/item/TMF_1979_41_3_a0/

[1] Yu. M. Shirokov, TMF, 39 (1979), 291 | MR | Zbl

[2] F. A. Berezin, Mat. sbornik, 60 (1963), 465 | MR

[3] R. A. Minlos, L. D. Faddeev, DAN SSSR, 141 (1961), 1335