In neutron optics, we analyse the propagation of slow (thermal) neutrons along a semi-infinite waveguide limited by a large repulsive potential (reminding the propagation of light along an optical fibre). We set an ideal case of a straight empty two-dimensional semi-infinite waveguide limited by an infinitely repulsive potential (Dirichlet conditions on its boundaries). The neutron wave function is given through an integral representation involving the incoming wave with energy E, Green’s function and certain functions defined on the boundaries. The latter functions follow from the Dirichlet conditions, thereby proposing a new formalism in neutron optics. We develop various approximations (through Fourier and Hilbert transforms) and numerical computations. We get: (a) the expected extinction of the incoming wave for very large penetration into the waveguide, (b) the generation of propagation modes and their number for suitably large penetration, as E increases, (c) an estimate of the critical angle.

中文翻译：

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中子光学中的中子波导：具有狄利克雷边界条件的格林函数形式主义

在中子光学中，我们分析了慢（热）中子沿着受大排斥势（提醒光沿着光纤传播）限制的半无限波导的传播。我们设置了一个理想情况，即由无限排斥势（其边界上的狄利克雷条件）限制的直空二维半无限波导。中子波函数是通过积分表示给出的，该积分表示涉及能量为 E 的入射波、格林函数和在边界上定义的某些函数。后一个函数遵循狄利克雷条件，从而提出了中子光学的新形式。我们开发了各种近似（通过傅立叶和希尔伯特变换）和数值计算。我们得到：