Scattering Phase Correction for Semiclassical Quantization Rules in Multi-Dimensional Quantum Systems

作     者：HUANG Wen-Min MOU Chung-Yu CHANG Cheng-Hung 

作者机构：Department of Physics National Tsing-Hua University Hsinchu Taiwan physics Division National Center for Theoretical Sciences Hsinchu Taiwan Institute of Physics National Chiao Tung University Hsinchu Taiwan Institute of Mathematical Modeling and Scientific Computing National Chiao Tung University Hsinchu Taiwan 

出 版 物：《Communications in Theoretical Physics》 (理论物理通讯（英文版）)

年 卷 期：2010年第53卷第2期

页      面：250-256页

核心收录：

学科分类：0809[工学-电子科学与技术（可授工学、理学学位）] 07[理学] 070205[理学-凝聚态物理] 08[工学] 070201[理学-理论物理] 0702[理学-物理学] 

基　　金：Supported by the National Science Council at Taiwan through Grants No. NSC 97-2112-M-009-008-MY3 

主　　题：Bogomolny's transfer operator semiclassical quantization rules quantum chaos 

摘      要：While the scattering phase for several one-dimensional potentials can be exactly derived, less is known in multi-dimensional quantum systems. This work provides a method to extend the one-dimensional phase knowledge to multi-dimensional quantization rules. The extension is illustrated in the example of Bogomolny＇s transfer operator method applied in two quantum wells bounded by step potentials of different heights. This generalized semiclassical method accurately determines the energy spectrum of the systems, which indicates the substantial role of the proposed phase correction. Theoretically, the result can be extended to other semiclassical methods, such as Gutzwiller trace formula, dynamical zeta functions, and semielassical Landauer Buttiker formula. In practice, this recipe enhances the applicability of semiclassical methods to multi-dimensional quantum systems bounded by general soft potentials.