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

We consider the Cauchy problems for Schrodinger 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 Schrodinger equations without a harmonic oscillator.