Boundary integral method for stationary states of two-dimensional quantum systems

Ioan Kosztin, Klaus Schulten

Research output: Contribution to journalArticlepeer-review


The boundary integral method for calculating the stationary states of a quantum particle in nano-devices and quantum billiards is presented in detail at an elementary level. According to the method, wave functions inside the domain of the device or billiard are expressed in terms of line integrals of the wavefunction and its normal derivative along the domain's boundary; the respective energy eigenvalues are obtained as the roots of Fredholm determinants. Numerical implementations of the method are described and applied to determine the energy level statistics of billiards with circular and stadium shapes and demonstrate the quantum mechanical characteristics of chaotic motion. The treatment of other examples as well as the advantages and limitations of the boundary integral method are discussed.

Original languageEnglish (US)
Pages (from-to)293-325
Number of pages33
JournalInternational Journal of Modern Physics C
Issue number2
StatePublished - Apr 1997


  • Billiard Systems
  • Boundary Element Method
  • Green's Functions
  • Quantum Chaos
  • Schrödinger Equation

ASJC Scopus subject areas

  • Computational Theory and Mathematics
  • Computer Science Applications
  • Mathematical Physics
  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics


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