Czechoslovak Journal of Physics B

, Volume 39, Issue 11, pp 1181–1191 | Cite as

On existence of a bound state in an L-shaped waveguide

  • P. Exner
  • P. Šeba
  • P. Št'oviček


We investigate the Laplace operator in an L-shaped strip of a widthd with Dirichlet boundary conditions. It is shown that it has a unique eigenvalue corresponding to a square-integrable eigenfunction, namely λ = 0·93 (π/d)2. This result has implications for the theory of waveguides as well as for electron motion in some microscopic semiconductor devices.


Boundary Condition Dirichlet Boundary Laplace Operator Dirichlet Boundary Condition Semiconductor Device 
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Copyright information

© Academia, Publishing House of the Czechoslovak Academy of Sciences 1989

Authors and Affiliations

  • P. Exner
    • 1
  • P. Šeba
    • 1
  • P. Št'oviček
    • 1
  1. 1.Laboratory of Theoretical PhysicsJoint Institute for Nuclear ResearchDubnaUSSR

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