Keywords
- Basic Equation
- Asymptotic Formula
- Ordinary Linear Differential Equation
- Modern Mathematical Physic
- Resolvent Estimate
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, access via your institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Agmon, S.: Spectral properties of Schrodinger operators and scattering theory, Ann. Scuola Norm. Sup. Pisa Sci. Mat. (1975), 151–218.
Benz-Artzi, M. and Devinatz, A.: Spectral and scattering theory for the adiabatic oscillator and related potentials, J. Math. Phys. 111(1979), 594–607.
Devinatz, A. and Rejto, P.: A limiting absorption principle for Schrodinger operators with oscillating potentials. I.J. Diff. Equations. 49, (1983), 85–104.
Devinatz, A. and Rejto, P.: A Limiting absorption Principle for Schrodinger operators with oscillating potentials. II. J. Diff. Equations. 49, (1983), 85–104.
Erdelyi, A.: Asymptotic Expansions. Dover, New York, 1956.
Pauli Lectures on Physics, Vol. 5, Wave Mechanics, Enz, C., P., (Ed.), MIT Press, Cambridge, Mass. 1977, See Sect. 27, The WKB-method.
Jager, W. and Rejto, P.: On the absolute continuity of the spectrum of Schrodinger operators with long range potentials. Oberwolfach Tagungsberichte, 17.7.-23.7. 1977.
Jager, W. and Rejto, P.: Limiting absorption principle for some Schrodinger operators with exploding potentials I. J. Math. Anal. Appl. 91(1983), 192–228.
Jager, W. and Rejto, P.: Limiting absorption principle for some Schrodinger operators with exploding potentials II. J. Math. Anal. Appl. 95 (1983), 169–194.
Kato, T.: Perturbation Theory for Linear Operators, Springer-Verlag, 1973.
Langer, R.E.: The asymptotic solutions of ordinary linear differential equations for the second order with special reference to a turning point. Trans. Amer. Math. Soc. 67 (1949), 461–490.
Mochizuki, M., and Uchiyama, J.: Radiation conditions and spectral theory for 2-body Schrodinger operators with “oscillating” long range potentials I. J. Math. Kyoto Univ. 18(2) (1978), 377–408.
Reed. M., and Simon, B.: Analysis of operators, Methods of Modern Mathematical Physics. Vol. IV, Academic Press. 1978, Section XIII.13, Example 1.
Saito, Y.: On the asymptotic behavior of the solutions of the Schrodinger equation. Osaka. J. Math. 14 (1977), 11–35. See the Ricatti equation (3.11).
Saito, Y.: Schrodinger Operators with a nonspherical radiation condition, to appear.
Saito, Y.: These Proceedings.
von Neumann, J. and Wigner, E.: Über merkwurdige diskrete Eigenwerte. Phys. Zschr 30(1929), 465–467.
Olver, F., T.,W.: Asymptotics and Special Functions. Academic Press. 1974.
Wasov, W.: Asymptotic Expansions for Ordinary Differential Equations. Wiley-Interscinec, 1965.
Devinatz, A., Moeckel, R., and Rejto, P.: A Wronskian Estimate For Schrodinger Operators With von Neumann-Wigner Type Potentials. Univ. Minn. Math. Report 1986.
Atkinson, F.: Discrete and Continuous Boundary Problems, Academic Press 1964, See Theorem 88.1.
Atkinson, F.: The asymptotic solutions of second order differential equations, Ann. Mat. Pura Appl. 37 (1954), 347–378.
Isozaki, Hiroshi: On the generalized Fourier transform associated with Schrodinger operators with long-range perturbations. J. reine angewandte Math. 337 (1982), 18–67.
Reed, M. and Simon, B.: Scattering Theory. Methods of Modern Mathematical Physics Vol. III, Academic Press 1979. See Section XI.8 and the notes to it where references to the original works of Natveev-Skriganov, Combescure-Ginibre and Schechter are also given.
Harris, W.A. and Lutz, D.A. A unified theory of asymptotic integration. J. Math. Anal. Appl. 57 (1977), 571–586.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1987 Springer-Verlag
About this paper
Cite this paper
Devinatz, A., Moeckel, R., Rejto, P. (1987). On Schrödinger operators with von Neumann-Wigner type potentials. In: Knowles, I.W., Saitō, Y. (eds) Differential Equations and Mathematical Physics. Lecture Notes in Mathematics, vol 1285. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0080584
Download citation
DOI: https://doi.org/10.1007/BFb0080584
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-18479-9
Online ISBN: 978-3-540-47983-3
eBook Packages: Springer Book Archive
