arXiv quant-ph/98070601998-07quant-ph

量子力学中的复参数

Complex Parameters in Quantum Mechanics

Giampiero Esposito

备注：: 17 pages, plain Tex. The revised version is much longer, and section 5 is entirely new
发表信息：: Found.Phys.Lett. 11 (1998) 535-547

摘要：

本文研究了任意空间维数q下中心势定态的薛定谔方程。在转换成一个等效方程后，一阶导数的系数为零，它表明，在这样的方程中，r的第二次逆幂的系数是一个参数的偶函数，比方说，λ，依赖于q和角动量量子数的线性组合，比方说，l。因此，在散射理论中有用的λ的复值的情况通常涉及最初被视为空间维度的参数的复值和角动量量子数的复值。本文最后证明了Levinson定理在任意数量的空间维度，当潜在的包括一个非局部项，这可能是有用的理解两个核子之间的相互作用。

英文摘要：

The Schrodinger equation for stationary states in a central potential is studied in an arbitrary number of spatial dimensions, say q. After transformation into an equivalent equation, where the coefficient of the first derivative vanishes, it is shown that in such equation the coefficient of the second inverse power of r is an even function of a parameter, say lambda, depending on a linear combination of q and of the angular momentum quantum number, say l. Thus, the case of complex values of lambda, which is useful in scattering theory, involves, in general, both a complex value of the parameter originally viewed as the spatial dimension and complex values of the angular momentum quantum number. The paper ends with a proof of the Levinson theorem in an arbitrary number of spatial dimensions, when the potential includes a non-local term which might be useful to understand the interaction between two nucleons.

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