标题： 互易定理和基本传递矩阵 显示英文标题

标题： Reciprocity Theorem and Fundamental Transfer Matrix

摘要： 静态势散射可以用由非厄米有效哈密顿量生成的量子动力学来表述。 我们利用这种表述来证明二维和三维情况下的互易定理，该证明不依赖于散射算符、格林函数或格林恒等式的性质。 特别是，我们将互易性与一个积分算子$\widehat{\mathbf{M}}$所满足的算符恒等式联系起来，该积分算子称为基本传递矩阵。 这是对一维势散射中传递矩阵$\mathbf{M}$的多维推广，该传递矩阵存储了势的散射振幅的信息。 我们利用$\widehat{\mathbf{M}}$的性质，该性质导致互易性，以确定二维和三维情况下关系$\det{\mathbf{M}}=1$的类似关系，并建立散射算符的一般反伪厄米性。 我们的结果适用于实势和复势。 显示英文摘要

摘要： Stationary potential scattering admits a formulation in terms of the quantum dynamics generated by a non-Hermitian effective Hamiltonian. We use this formulation to give a proof of the reciprocity theorem in two and three dimensions that does not rely on the properties of the scattering operator, Green's functions, or Green's identities. In particular, we identify reciprocity with an operator identity satisfied by an integral operator $\widehat{\mathbf{M}}$, called the fundamental transfer matrix. This is a multi-dimensional generalization of the transfer matrix $\mathbf{M}$ of potential scattering in one dimension that stores the information about the scattering amplitude of the potential. We use the property of $\widehat{\mathbf{M}}$ that is responsible for reciprocity to identify the analog of the relation, $\det{\mathbf{M}}=1$, in two and three dimensions, and establish a generic anti-pseudo-Hermiticity of the scattering operator. Our results apply for both real and complex potentials.