This paper is concerned with the efficient numerical computation of solutions to the 1D stationary Schrödinger equation in the semiclassical limit in the highly oscillatory regime. A previous approach to this problem based on explicitly incorporating the leading terms of the WKB approximation is enhanced in two ways: first a refined error analysis for the method is presented for a not explicitly known WKB phase, and secondly the phase and its derivatives will be computed with spectral methods. The efficiency of the approach is illustrated for several examples.

中文翻译：

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半经典极限中一维Schrödinger方程的WKB方法：增强相位处理

本文涉及在高振动状态下半经典极限中一维平稳Schrödinger方程解的有效数值计算。基于显式合并WKB逼近的主导项来解决此问题的先前方法以两种方式得到增强：首先，针对一个未知的WKB相位，对该方法进行了精确的误差分析，其次，将对该相位及其派生函数进行分析。用光谱法计算。通过几个示例说明了该方法的效率。