The name of ``spike" denotes a negative-power component in the
potential. Its extraordinary appeal in quantum model-building
ranges from phenomenology (it cannot be switched off smoothly) to
perturbation theory (one needs non-power-law expansions in general
-- cf. [9]). Many methods can be employed ranging from certain
strict algebraic considerations (yielding, e.g., quasi-exact
states -- cf. [19]) till the brute force numerical solutions. In
this framework, the paper under consideration applies, develops
and tests the idea (cf. [51] and several previous papers by the
present authors) of an analytic iterative construction of wave
functions via the Riccatian non-linear rearrangement of the linear
Schr\"{o}dinger equation. Such a method (called
quasilinearization) is shown to offer amazing numerical precision
of approximants already in its second iteration.

MR2351972 Liverts, E. Z.; Mandelzweig, V. B. Accurate analytic
presentation of solution for the spiked harmonic oscillator
problem. Ann. Physics 322 (2007), no. 9, 2211--2232. 81Q05




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%1 [27] 86xxxxx Znojil M, Roychoudhury R Spiked and screened
%oscillators V(r)=Ar-2+B/r(2)+C/r(4)+D/r(6)+F/(1+Gr)(2) and their
%elementary bound states CZECHOSLOVAK JOURNAL OF PHYSICS 48 (1):
%1-8 JAN
%1998 Times Cited: 10
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%[25] 1019 (M.F.Flynn, R. Guardiola and M.Z.) The spiked harmonic
%oscillator V (r) = r2 + ¸rĄ4 as a challenge to perturbation
%theory. Czech. J. Phys. 41 (1991) 1019-29. 1993
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%2 [38] 107xxxxx ZNOJIL M THE NONSINGULAR SPIKED
%HARMONIC-OSCILLATOR - COMMENT JOURNAL OF MATHEMATICAL PHYSICS 34
%(10): 4914-4914 OCT
%1993 Times Cited: 11
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%3 [22] 110xxxxx ZNOJIL M, LEACH PGL ON THE ELEMENTARY SCHRODINGER
%BOUND-STATES AND THEIR MULTIPLETS JOURNAL OF MATHEMATICAL PHYSICS
%33 (8): 2785-2794 AUG
%1992 Times Cited: 28
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%4 [21] 116xxxxx ZNOJIL M THE POTENTIAL V(R) = AR(2)+BR(-4)+CR(-6)
%AND A NEW METHOD OF SOLVING THE SCHRODINGER-EQUATION PHYSICS
%LETTERS A 158 (9): 436-440 SEP 23
%1991 Times Cited: 15
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%5 [37] 126xxxxx ZNOJIL M SINGULAR ANHARMONICITIES AND THE ANALYTIC
%CONTINUED FRACTIONS
%  2xxxxx THE POTENTIALS V(R)=AR2+BR-4+CR-6 JOURNAL OF MATHEMATICAL
%PHYSICS 31 (1): 108-112 JAN
%1990 Times Cited: 48
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%6 [36] 129xxxxx ZNOJIL M SINGULAR ANHARMONICITIES AND THE ANALYTIC
%CONTINUED FRACTIONS JOURNAL OF MATHEMATICAL PHYSICS 30 (1): 23-27
%JAN
%1989 Times Cited: 38
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%7 [20] 156xxxxx ZNOJIL M A NEW TREATMENT OF SINGULAR POTENTIALS
%PHYSICS LETTERS A 101 (2): 66-68
%1984 Times Cited: 9
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%8 [19] 167xxxxx ZNOJIL M ELEMENTARY BOUND-STATES FOR THE POWER-LAW
%POTENTIALS JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL 15 (7):
%2111-2122
%1982 Times Cited: 42
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%[25] 1019 1993