Schrödinger operators with moving point perturbations and related solvable models of quantum mechanical systems

Zeitschrift für Analysis und ihre Anwendungen

Volumn 17, Issue 1, 1998, Pages 37-55

  Geyler, V A ^a   Chudaev, I V ^a  

^a OGAREV MORDOVIA STATE UNIVERSITY   (Russian Federation)

Author keywords

Impurity in a well; Low dimensional systems in a magnetic field; Point perturbation; Schr dinger operators

Indexed keywords

EID: 2142669354     PISSN: 02322064     EISSN: None     Source Type: Journal    
DOI: 10.4171/ZAA/807     Document Type: Article

References (15)

1. Albeverio, S., Fenstad, J. E., Høegh-Kron, R. and T. Lindstrøm: Nonstandard Methods in Stochastic Analysis and Mathematical Physics. New York et al.: Academic Press 1986.
2. Albeverio, S., Gesztesy, F., Høegh-Krohn, R. and H. Holden: Solvable Models in Quantum Mechanics. Berlin et al.: Springer-Verlag 1988.
3. Altarelli, M.: Electronic states in semiconductor superlattices and quantum wells: an overview. In: Springer Ser. Solid-State Sci. (Electronic materials) (eds.: I. R. Chelikowsky and A. Franciosi). Berlin et al.: Springer-Verlag 95 (1991), 215 - 232.
4. Altarelli, M. and G. Platero: Magnetic hole levels in quantum wells in parallel magnetic field. Surf. Sci. 196 (1988), 540 - 544.
5. Ando, T., Fauler, A. and F. Stern: Electronic properties of two-dimensional systems. In: Rev. Modern Phys. 54 (1982), 437 - 672.
6. Bagwell, P. E. and R. K. Lake: Resonances in transmission through an oscillating barrier. Phys. Rev. B46 (1992), 15 329 - 15 336.
7. Beenakker, C. W. J. and H. van Houten: Quantum transport in semiconductor nanostructures. In: Solid State Phys., Advances in Res. and Appl. (eds.: II. Ehrenreich and D. Turnbull). Boston et al.: Acad. Press 44 (1991), 1 - 228.
8. De Dios Leyva, M. and V. Galindo: Interband optical absorption in superlattices in an in-plane magnetic field. Phys. Rev. B.48 (1993), 4518 - 4523.
9. Dunford, N. J. T. and Schwartz: Linear operators. Part II: Spectral Theory. New York et al.: Interscience 1963.
10. Gerard, G.-M. and J.-Y. Marzin: Optical study of probability densities in quantum well eigenstates. Surf. Sci. 229 (1990), 433 - 438.
11. Geyler, V. A. and I. V. Chudaev: The spectrum of a quasi-two-dimensional system in the presents of a parallel magnetic field (in Russian). Zhurn. Vych. Matem. i Matem. Fiz. 37 (1997)2, 214 - 222;
12. Engl. transl. in: Comput. Math, and Math. Phys. 37 (1997), 210 - 218.
13. Geyler, V. A., Margulis, V. A. and I. I. Chuchaev: Zero-range potentials and Carleman operators (in Russian). Sibir. Matem. Zhurnal 36 (1995), 828 - 841;
14. Engl. transl. in: Siberian Math. J. 36 (1995), 714 - 726.
15. Geyler, V. A., Margulis, V. A. and I. V. Chudaev: Harmonic oscillator with a moving point perturbation (in Russian). Matem. Modelirovanie 7 (1995)5, p. 45.