Abstract
The quantal problem of a particle interacting in one dimension with an external time-dependent quadratic potential and a constant inverse square potential is exactly solved. The solutions are found both in the Schrödinger representation, by using a generating function or a time-dependent raising operator, and in the Heisenberg picture. They depend only on the solution of the classical harmonic oscillator. The generalizations to the n-dimensional problem and to the problem of N particles in one dimension, interacting pairwise via a quadratic time-dependent potential and a constant inverse square potential, are finally sketched.
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