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Quasiexactly solvable quartic: elementary integrals and asymptotics
, 2011
"... Littlewood, when he makes use of an algebraic identity, always saves himself the trouble of proving it; he maintains that an identity, if true, can be verified in few lines by anybody obtuse enough to feel the need of verification. Freeman Dyson [7] We study elementary eigenfunctions y = pe h of ope ..."
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Cited by 6 (6 self)
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Littlewood, when he makes use of an algebraic identity, always saves himself the trouble of proving it; he maintains that an identity, if true, can be verified in few lines by anybody obtuse enough to feel the need of verification. Freeman Dyson [7] We study elementary eigenfunctions y = pe h of operators L(y) = y ′ ′ + Py, where p, h and P are polynomials in one variable. For the case when h is an odd cubic polynomial, we investigate the real level crossing points and asymptotics of eigenvalues. This study leads to an interesting identity with elementary integrals.
Twoparametric PTsymmetric quartic family
, 2011
"... We describe a parametrization of the real spectral locus of the twoparametric family of PTsymmetric quartic oscillators. For this family, we find a parameter region where all eigenvalues are real, extending ..."
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Cited by 2 (2 self)
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We describe a parametrization of the real spectral locus of the twoparametric family of PTsymmetric quartic oscillators. For this family, we find a parameter region where all eigenvalues are real, extending
SPECTRAL LOCI OF STURM–LIOUVILLE OPERATORS WITH POLYNOMIAL POTENTIALS
, 2012
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