Scattering phase correction for semiclassical quantization rules in multi-dimensional quantum systems

Wen Min Huang, Chung Yu Mou, Cheng-Hung Chang*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


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 semiclassical Landauer-Büttiker formula. In practice, this recipe enhances the applicability of semiclassical methods to multi-dimensional quantum systems bounded by general soft potentials.

Original languageEnglish
Pages (from-to)250-256
Number of pages7
JournalCommunications in Theoretical Physics
Issue number2
StatePublished - 26 Feb 2010


  • Bogomolny's transfer operator
  • Quantum chaos
  • Semiclassical quantization rules


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