DYNAMICAL EFFECTIVE POTENTIAL FOR TUNNELING - AN EXACT MATRIX-METHOD AND A PATH-INTEGRAL TECHNIQUE

The dynamical effective potential felt by an electron tunneling in a o ne-dimensional model STM junction is considered. The electron is coupl ed inside the barrier to surface plasmons. The corresponding many body Schrodinger equation is solved exactly by means of a matrix method. R esults for the electron effective potential and for tunneling times ar e presented. They are compared to calculations for the same model barr ier described within the path integral formalism. As is well known, si gnificant differences from the corresponding static image potential ar e obtained when tunneling times are shorter than the inverse surface p lasmon frequency. However, our results show that path integral calcula tions underestimate the tunneling traversal time, leading to a larger effective electron potential relative to that obtained by the matrix m ethod.