Boundary Integral Method for Stationary States of Two-Dimensional Quantum Systems

Ioan Kosztin () and Klaus Schulten ()
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Ioan Kosztin: Department of Physics, University of Illinois at Urbana-Champaign 1110 West Green Street, Urbana, Illinois 61801, USA
Klaus Schulten: Department of Physics, University of Illinois at Urbana-Champaign 1110 West Green Street, Urbana, Illinois 61801, USA

International Journal of Modern Physics C (IJMPC), 1997, vol. 08, issue 02, 293-325

Abstract: Theboundary integral methodfor 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.

Keywords: Boundary Element Method; Schrödinger Equation; Billiard Systems; Quantum Chaos; Green's Functions (search for similar items in EconPapers)
Date: 1997
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DOI: 10.1142/S0129183197000278

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