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Semilinear Schrödinger evolution equations with inverse-square and harmonic potentials via pseudo-conformal symmetry

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  • We consider the Cauchy problems for Schrödinger equations with an inverse-square potential and a harmonic one. Since the Mehler type formulas are completed, the pseudo-conformal transforms can be constructed. Thus we can convert the problems into the nonautonomous Schrödinger equations without a harmonic oscillator.

    Mathematics Subject Classification: Primary: 35Q55, 35Q40; Secondary: 81Q15.


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