One of the students of my labo and I have been studying the field emission from carbon nanotubes (CNTs). This emission is the current of electrons from a CNT by quantum tunneling. The emission rate is given by the FN formula.
We are now thinking an extension of this formula by introduing a time-dependent term and/or a 1/x term. We expect that we can obtain analytic solutions using an application of the LR method which is a strong method to construct analytic solutions for time-dependent harmonic oscillators systematically.