SPECTRAL ZETA FUNCTIONS OF A 1D SCHRÖDINGER PROBLEM
SPECTRAL ZETA FUNCTIONS OF A 1D SCHRÖDINGER PROBLEM
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一维薛定谔问题的光谱 Zeta 函数
DOI：
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发表时间：
2011
期刊：
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通讯作者：
Joseph D. Watkins
中科院分区：
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作者：
Joseph D. Watkins
我们研究了与势V(X)=x2M+αxm-1+(λ2-1/4)/x2的径向薛定谔问题有关的谱zeta函数。在直接计算某些Zeta函数后，我们使用量子Wronskian方程给出它们之间的求和规则，允许实例中Zeta函数的显式形式可以被简化。这项工作的一个直接应用是导出涉及超几何级数的函数关系和恒等式，允许找到已知恒等式作为更一般结果的实例。然后将我们的工作推广到一类相关的对称特征值问题。利用融合量子Wronskian，我们给出了一种间接计算伴随谱Zeta函数的简单方法。然后将这种方法应用于计算运动的非局域积分Gn，它出现在一个相关的可积量子场论中。
We study the spectral zeta functions associated to the radial Schrödinger problem with potential V(x) = x2M + αxM-1 + (λ2 - 1/4)/x2. After directly computing some of the zeta functions, we use the quantum Wronskian equation to give sum rules between them, allowing for instances where the explicit form of the zeta functions can be simplified. An immediate application of this work is to derive functional relations and identities involving hypergeometric series, allowing for known identities to be found as instances of more general results. Our work is then extended to a class of related -symmetric eigenvalue problems. Using the fused quantum Wronskian, we give a simple method for indirectly calculating the associated spectral zeta functions. This method is then applied to calculate the nonlocal integrals of motion Gn which appear in an associated integrable quantum field theory.