Abstract
Under some hypotheses of analyticity and integrability we show the existence and uniqueness of a strong regular solution of the Schrödinger equation using a natural generalisation to the complex case of the Feynman-Kac formula. This explicit representation allows us to study in certain cases the asymptotic behavior of the solution when the Planck constanth tends to zero. The same method can be used for the solution of more general Schrödinger equations.
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Transmis par J. Ginibre
Membre du Laboratoire Associé au C.N.R.S., n° 224 ≪Processus Stochastiques et Applications≫
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Doss, H. Sur une Resolution Stochastique de l'Equation de Schrödinger à Coefficients Analytiques. Commun.Math. Phys. 73, 247–264 (1980). https://doi.org/10.1007/BF01197701
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DOI: https://doi.org/10.1007/BF01197701