Quantum tunnelling from a metastable potential: the driven Morse potential

We study the behaviour of a particle in a Morse potential under the influence of an external force. We have chosen the Morse potential as an example for an anharmonic potential since the eigenvalues, eigenfunctions and dipole matrix elements can be calculated analytically. Based on these results we solve the time-dependent Schroedinger equation for the driven system numerically. In the first step we use a time-dependent external force to induce transitions from the ground state to an excited state, for example to an energy eigenstate. In the second step we apply a constant external force to enable quantum tunneling through an energy barrier whose height can be tuned by changing the external force. We investigate quantum tunnelling for various excited states, in particular energy eigenstates.