Quantum tunnelling effect for the inverted Caldirola-Kanai Hamiltonian

In order to study the behaviour of the inverted Caldirola-Kanai Hamiltonian in the quantum tunnelling effect, the authors consider a wavepacket as the initial state and they calculate exactly the probability density. They also obtain the transmission and reflection probability, the expectation value of the particle's energy and the sojourn time which appears to be an increasing function of the dissipation parameter gamma . A similar result is also obtained by considering a normalized plane wave as the initial state.