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

Abstract

The object of this article is to study the separation of the Schrödinger operator A of the form

with operator potential V(x) ∈ C ¹ (Rⁿ , L (H ₁)), in the Hilbert space H = L ₂(Rⁿ , H ₁), where L (H ₁) is the space of all bounded linear operators on H ₁ and

is the Laplace operator in Rⁿ . Moreover, we study the existence and uniqueness of the solution of the Schrödinger equation

in the space H.

Keywords:

• Separation
• Schrödinger operator
• Hilbert space
• Coercive estimate
• AMS Mathematics Subject Classifications: 47F05
• 58J99

Notes

E-mail: [email protected]

Additional information

Notes on contributors

H.A. Atia †

E-mail: [email protected]