Separation of the Schrödinger operator with an operator potential in the Hilbert spaces

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In this Subject: <a title="Mathematics and Statistics" href="/content/subcat?j_subject=195&j_availability=">Mathematics and Statistics
By this author: A.S. Mohamed ;&nbsp; H.A. Atia

Authors: A.S. Mohamed; H.A. Atia

Source: Applicable Analysis, Volume 84, Number 1, January 2005 , pp. 103-110(8)

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Abstract:

The object of this article is to study the separation of the Schrödinger operator A of the form with operator potential V ( x ) isin

C 1 ( R n , L ( H 1 )), in the Hilbert space H = L 2 ( R n , H 1 ), where L ( H 1 ) is the space of all bounded linear operators on H 1 and is the Laplace operator in R n . Moreover, we study the existence and uniqueness of the solution of the Schrödinger equation in the space H .