Abstract
LetV be any (sufficiently regular) attractive potential in one and two dimensions. We make rigorous an argument of M. Kac [1], relating the recurrence of the Brownian motion to the existence of at least one bound state for the quantum HamiltonianH = −(δ/2)+ V.
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Ruelle, P. Brownian local time and quantum mechanics. J Stat Phys 43, 609–620 (1986). https://doi.org/10.1007/BF01020655
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DOI: https://doi.org/10.1007/BF01020655