Abstract
An algebraic method to solve the time-dependent inverted harmonic oscillator (TDIHO) is proposed, and the analytical expressions of the wavefunctions obtained by this method are suitable for discussion of the quantum tunneling effect. With the Gaussian wave packet as the initial state, the general expressions of transmission and reflection probabilities, and dwell time of TDIHO are obtained. The quantum tunneling effect is further illustrated through two specific cases.
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