Abstract
The time evolution of a time-dependent inverted harmonic oscillator (TDIHO) of arbitrary dimensions is investigated. Using the algebraic method, we obtain the exact orthogonal basis of solutions of a TDIHO in which the dimensionality d and angular momentum l appear as parameters, and also discuss its properties. With the wavepacket as the initial state, the general expressions of sojourn time of a TDIHO are given. The method is also applied to the inverted Caldirola–Kanai harmonic oscillator. The results show that the sojourn time appears as an increasing function of the dissipation parameter in arbitrary dimensions, but a decreasing function of the dimensionality.
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