The Cauchy problem of the one dimensional Schrödinger equation with non-local potentials

I. E. Kougias

International Journal of Mathematics and Mathematical Sciences, 1993, vol. 16, 1-4

Abstract:

For a large class of operators A , not necessarily local, it is proved that the Cauchy problem of the Schrödinger equation: − d 2 f ( z ) d z 2 + A f ( z ) = s 2 f ( z ) , f ( 0 ) = 0 , f ′ ( 0 ) = 1 possesses a unique solution in the Hilbert ( H 2 ( Δ ) ) and Banach ( H 1 ( Δ ) ) spaces of analytic functions in the unit disc Δ = { z : | z | < 1 } .

Date: 1993
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:316456

DOI: 10.1155/S0161171293000985

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