Abstract
The existence of bound states in a plane quantum waveguide is proved under weak conditions: Within a bounded set a more general shape than a curved parallel strip is admitted and the curvature of the reference curve need not be differentiable. Furthermore, no upper bound for the width of the strip is required.
Similar content being viewed by others
References
Agmon, S.:Lectures on Elliptic Boundary Value Problems, van Nostrand, Princeton, N.J., 1965.
Ashbaugh, M. S. and Exner, P.: Lower bounds to bound state energies in bent tubes,Phys. Lett. A 150, 83 (1990).
Duclos, P. and Exner, P.: Curvature vs. thickness in quantum waveguides,Czech. J. Phys. 41, 1009 (1991).
Edmunds, D. E. and Evans, W. D.:Spectral Theory and Differential Operators, Clarendon Press, Oxford, 1987.
Exner, P. and Šeba, P.: Bound states in curved quantum waveguides,J. Math. Phys. 30, 2574 (1989).
Exner, P.: Bound states and resonances in quantum wires,Adv. Operator Theory 46, 65 (1990).
Exner, P.: Bound states in quantum waveguides of a slowly decaying curvature,J. Math. Phys. 34, 23 (1993).
Exner, P., Šeba, P., and Štoviček, P.: On existence of a bound state in an L-shaped waveguide,Czech. J. Phys. B 39, 1181 (1989).
Goldstone, J. and Jaffe, R. L.: Bound states in twisting tubes,Phys. Rev. B 45, 14100 (1992).
Reed, M. and Simon, B.:Methods of Modern Mathematical Physics, Vol. I: Functional Analysis (rev. edn.), Academic Press, New York, 1980.
Reed, M. and Simon, B.:Methods of Modern Mathematical Physics, Vol II: Fourier Analysis, Self-Adjointness, Academic Press, New York, 1975.
Reed, M., Simon, B.:Methods of Modern Mathematical Physics, Vol. IV: Analysis of Operators, Academic Press, New York, 1978.
Renger, W.: Diplomarbeit, Techn. Univ. Graz, June 1993.
Ziemer, W. P.:Weakly Differentiable Functions, Springer-Verlag, New York, 1989.