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arXiv · 1510.03786

Green kernel for a random Schr\"odinger operator

Carlos G. Pacheco
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Abstract

We find explicitly the Green kernel of a random Schr\"odinger operator with Brownian white noise. To do this, we first handle the random operator by defining it weakly using the inner product of a Hilbert space. Then, using classic Sturm-Liouville theory, we can build the Green kernel with linearly independent solutions of a homogeneous problem. As a corollary we have that the random operator has a discrete spectra.

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Carlos G. Pacheco. 2015-10-13. Green kernel for a random Schr\"odinger operator. https://doi.org/10.1142/s0219199715500820

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