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Schrödinger operators with magnetic and electric potentials

Published online by Cambridge University Press:  17 April 2009

Yu Kaiqi
Yu Kaiqi
Affiliation:
Department of Mathematics, Physics and Mechanics NanjingUniversity of Aeronautics and Astronautics Nanjing210016 People'sRepublic of China
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Abstract

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In the present paper, we consider Schrödinger operators which are formally given by . In Section 2 and 3 we prove that P has a regularly accretive extension which is a self-adjoint extension of P and it is the only self-adjoint realisation of P in L2 (RN) when satisfies = (a1, a2, …, aN) ∈ , aj, real-valued, , real-valued and the negative part V-:= max(0, -V) satisfys , with constants 0 ≤ C1 < 1, C2 ≥ 0 independent of V. In Section 4, we prove that P is essential self-adjoint on when , V sat0isfy ; V = V1 + V2, V real-valued, , i = 1, 2, V1(x) ≥ –C |x|2, for x ∈ RN with C ≥ 0 and 0 ≥ V2 ∈ KN.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 50 , Issue 2 , October 1994 , pp. 299 - 312
Copyright
Copyright © Australian Mathematical Society 1994

References

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