论文部分内容阅读
While the scattering phase for several one-dimensional potentials can be exactly derived, less is knownin multi-dimensional quantum systems. This work provides a method to extend the one-dimensional phase knowledgeto multi-dimensional quantization rules. The extension is illustrated in the example of Bogomolny’s transfer operatormethod applied in two quantum wells bounded by step potentials of different heights. This generalized semiclassicalmethod accurately determines the energy spectrum of the systems, which indicates the substantial role of the proposedphase correction. Theoretically, the result can be extended to other semiclassical methods, such as Gutzwiller traceformula, dynamical zeta functions, and semielassical Landauer-Buttiker formula. In practice, this recipe enhances theapplicability of semiclassical methods to multi-dimensional quantum systems bounded by general soft potentials.
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 semiclassicalmethod directly 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 traceformula, dynamical zeta functions, and semielassical Landauer-Buttiker formula. In practice, this recipe enhances theapplicability of semiclassical methods to multi-dimensional quantum systems bounded by general soft potentials.