Abstract
Field emission from a monatomic tip in scanning tunneling microscopy (STM) is modeled by a zero-range potential in the presence of a static constant electric field, a problem that has an exact analytic solution. The model yields an electron current that compares favorably to experimental results as well as more sophisticated theoretical models used to describe STM. The width of the current density at the end of the classically forbidden region is identified. A Gaussian wave packet starting from the end of the tunnel with this width provides an excellent description of the ensuing electron motion. Next, changing the subject, exact zero-range potential calculations of high-harmonic generation in an elliptically polarized laser field are presented. These calculations are then modeled in terms of Gaussian wave packets whose centers follow classical electronic orbits that originate from and return to the ionic core. For the initial widths of these wave packets the width derived above in the context of STM is used. Good agreement with the exact harmonic rates is obtained from the tunneling regime well into the multiphoton regime.
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