Abstract
References
- Albeverio, G., Gesztesy, F., Hoegh-Krohn, R. and Holden,H. Solvable Models in Quantum Mechanics (2nd edition) (AMS Chelsa Publishing, Providence, RI, 2005).
- Berezin, F. A. and Faddeev, L. D. Remarks on Schr¨odinger equation with singular potential, Dokl. Akad. Nauk. 137 (7), 1011–1014, 1961 (in Russian).
- Birman, M. Sh. and Solomyak, M. Z. Spectral Theory of Self-adjoint Operators in Hilbert Space (D. Reidel Pulb.Co., Dordrecht, Holland, 1987).
- Eastham, M. S. P. The Spectral Theory of Periodic Differential Equations (Scottish Aca- demic Press, Edinburgh, London, 1973).
- Hryniv, R. O. Analyticity and uniform stability in the inverse spectral problem for impedanse Sturm-Lioville operators, Carpatian Mathematical Publications 2 (1), 35–58, 2010.
- Kato, T. Theory of Perturbation of Linear Operators (M.:Mir, 1972).
- Knyazev, P. N. On the use of minimax properties in perturbation theory, Russian Mathe- matics (˙Izvestiya VUZ. Matematika) 2, 94–100, 1959.
- Korotyaev, E. Inverse problem for periodic “weighted” operators, J. Functional Analysis , 188–218, 2000.
- Minlos, R. A. and Faddeev, L. D. On pointwise interaction for a system of three particles in Quantum Mechannics, Dokl. Akad. Nauk. 141 (6), 1335–1338, 1961 (in Russian).
- Naimark, M. A. Linear Differential Operators (Frederick Ungar Publ. Co., New York, 1968).
- Titchmarsh, E. C. Eigenfunction Expansions Associated with Second Order Differential Equations, Part II. 2nd Ed. (Clarendon Press, Oxford, 1962).
- Vladimirov, V. S. Generalized Functions in Mathematical Physics (M.: Nauka, 1976) (in Russian).
Abstract
The number of negative eigenvalues of the “weighted” Schr¨odinger operator with point δ-interactions are found and by means of the Floquet theory, stability or instability of the solutions to periodic “weighted” equations with δ-interactions are determined.
Keywords
“Weighted” Schr¨odinger operator Point δ-interactions Negative eigenvalues 2000 AMS Classification: 47 A 10
References
- Albeverio, G., Gesztesy, F., Hoegh-Krohn, R. and Holden,H. Solvable Models in Quantum Mechanics (2nd edition) (AMS Chelsa Publishing, Providence, RI, 2005).
- Berezin, F. A. and Faddeev, L. D. Remarks on Schr¨odinger equation with singular potential, Dokl. Akad. Nauk. 137 (7), 1011–1014, 1961 (in Russian).
- Birman, M. Sh. and Solomyak, M. Z. Spectral Theory of Self-adjoint Operators in Hilbert Space (D. Reidel Pulb.Co., Dordrecht, Holland, 1987).
- Eastham, M. S. P. The Spectral Theory of Periodic Differential Equations (Scottish Aca- demic Press, Edinburgh, London, 1973).
- Hryniv, R. O. Analyticity and uniform stability in the inverse spectral problem for impedanse Sturm-Lioville operators, Carpatian Mathematical Publications 2 (1), 35–58, 2010.
- Kato, T. Theory of Perturbation of Linear Operators (M.:Mir, 1972).
- Knyazev, P. N. On the use of minimax properties in perturbation theory, Russian Mathe- matics (˙Izvestiya VUZ. Matematika) 2, 94–100, 1959.
- Korotyaev, E. Inverse problem for periodic “weighted” operators, J. Functional Analysis , 188–218, 2000.
- Minlos, R. A. and Faddeev, L. D. On pointwise interaction for a system of three particles in Quantum Mechannics, Dokl. Akad. Nauk. 141 (6), 1335–1338, 1961 (in Russian).
- Naimark, M. A. Linear Differential Operators (Frederick Ungar Publ. Co., New York, 1968).
- Titchmarsh, E. C. Eigenfunction Expansions Associated with Second Order Differential Equations, Part II. 2nd Ed. (Clarendon Press, Oxford, 1962).
- Vladimirov, V. S. Generalized Functions in Mathematical Physics (M.: Nauka, 1976) (in Russian).
Details
| Primary Language | English |
|---|---|
| Subjects | Statistics |
| Journal Section | Mathematics |
| Authors | |
| Publication Date | May 1, 2012 |
| Published in Issue | Year 2012 Volume: 41 Issue: 5 |