Quantization conditions in Bogomolny’s transfer operator method

Cheng-Hung Chang*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


Bogomolny’s transfer operator method plays a significant role in the study of quantum chaos, along with other well known methods like Gutzwiller’s trace formula and the dynamical zeta function, which generalize the Einstein-Brillouin-Keller quantization rule from integrable systems to chaotic systems. According to the theory, the Fredholm determinant of the transfer operator, defined on a Poincaré section of a classical physical system, provides a quantization condition to the energy spectrum of the corresponding quantum system. This study presents two factorization formulas, which relate different quantization conditions defined on different classical trajectory segments. These explicit relations answer the question of why all these classical quantization conditions determine exactly the same energy spectrum of the corresponding quantum systems. As an example, these formulas are illustrated in the equilateral triangular billiard.

Original languageEnglish
Number of pages1
JournalPhysical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Issue number5
StatePublished - 20 Nov 2002


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