On the Inverse Problem in Quantum Scattering Theory
On the Inverse Problem in Quantum Scattering Theory
复制标题
量子散射理论中的反问题
DOI：
10.1002/qua.560280842
复制
发表时间：
2009
影响因子：
2.2
通讯作者：
N. Elander
中科院分区：
文献类型：
--
作者：
E. Brändas;E. Engdahl;Magnus Rittby;N. Elander
讨论了量子散射理论中反问题的Gelfand-Levitan公式的完备性和解析延拓。经典的绿色的功能和相关的完整性关系的Titchmarsh-Weyl框架内进行了分析。Titchmarsh-Weyl公式的一个有吸引力的特点是，为了揭示复平面中的共振结构，可以将复标度引入一组相当一般的电位。此外，这一过程允许的经典绿色的功能和相关的完整性关系的分析扩展。广义完备关系可用于构造Gel'fand-Levitan积分方程的核。除了提供一个可能性测试completenesb性质的广义扩展也可以找到反演公式的潜力，表现出分析扩展到某些部门在复平面。作为一个测试，我们分析了一个简单的指数势，发现它包含了一个完整的字符串的复杂的能量共振与由此产生的广义谱密度受到一个特定的紧缩属性。
The Gel’fand-Levitan formulation of the inverse problem in quantum scattering theory is discussed with respect to completeness and analytic extensions. The classic Green’s function and the associated completeness relation are analyzed within the Titchmarsh-Weyl framework. An attractive feature of the Titchmarsh-Weyl formulation concerns the possibility to invoke complex scaling to a rather general set of potentials in order to expose resonance structures in the complex plane. In addition this procedure allow for an analytic extension of the classic Green’s function and the associated completeness relation. The generalized completeness relation can be used to construct the kernels of the Gel’fand-Levitan integral equation. In addition to supplying a possibility for testing completenesb properties of generalized expansions one may also find inversion formulas for potentials that exhibit analytic extensions to some sector in the complex plane. As a test we have analyzed a simple exponential potential which was found to contain a whole string of complex energy resonances with the resulting generalized spectral density being subjected to a particular deflation property.