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A trace formula for schrödinger operators with step potentials

Published online by Cambridge University Press:  17 February 2009

D. M. O'Brien
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Abstract

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This paper shows how to compute the trace of G(T) – G(T0), where G is an infinitely differentiable function with compact support, and where T and T0 are one-dimensional Schrödinger operators on (−∞, ∞) with potentials q and q0. It is assumed that q0 is a simple step potential and that q decays exponentially to q0. The trace is expressed in terms of the reflection and transmission coefficients for the scattering of plane waves by the potential q.

Type
Research Article
Information
The ANZIAM Journal , Volume 24 , Issue 2 , October 1982 , pp. 138 - 159
Copyright
Copyright © Australian Mathematical Society 1982

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