Ian Jauslin

Exact solution of the Schrodinger equation for photoemission from a metal

Ovidiu Costin, Rodica Costin, Ian Jauslin, Joel L. Lebowitz



We solve rigorously the time dependent Schrödinger equation describing electron emission from a metal surface by a laser field perpendicular to the surface. We consider the system to be one-dimensional, with the half-line \(x<0\) corresponding to the bulk of the metal and \(x>0\) to the vacuum. The laser field is modeled as a classical electric field oscillating with frequency \(\omega\), acting only at \(x>0\). We consider an initial condition which is a stationary state of the system without a field, and, at time \(t=0\), the field is switched on. We prove the existence of a solution \(\psi(x,t)\) of the Schr\"odinger equation for \(t>0\), and compute the surface current. The current exhibits a complex oscillatory behavior, which is not captured by the ``simple'' three step scenario. As \(t\to\infty\), \(\psi(x,t)\) converges with a rate \(t^{-\frac32}\) to a time periodic function with period \(\frac{2\pi}{\omega}\) which coincides with that found by Faisal, Kamiński and Saczuk (Phys Rev A 72, 023412, 2015). However, for realistic values of the parameters, we have found that it can take quite a long time (over 50 laser periods) for the system to converge to its asymptote. Of particular physical importance is the current averaged over a laser period \(\frac{2\pi}\omega\), which exhibits a dramatic increase when \(\hbar\omega\) becomes larger than the work function of the metal, which is consistent with the original photoelectric effect.



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The data for the figures in this paper was obtained using the program 'photocomp', which I wrote, but is not released yet. Stay tuned!

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