Inverse and Algebraic Quantum Scattering Theory pp 342-353 | Cite as
Exactly solvable quantum models for investigation of nonadiabatic transitions
Conference paper
First Online:
Abstract
The generalized technique of Bargmann potentials is applied for the reconstruction of time-dependent and time-independent two-dimensional potentials and corresponding solutions in a closed analytic form on the basis of the inverse scattering problem in the adiabatic representation. Matrix elements of the induced gauge potentials can be constructed and studied in terms of obtained exact solutions. The approach suggested permits investigation of the dynamical quantum transition amplitudes for spectral data with a prescribed dependence on parametric coordinate variables.
Preview
Unable to display preview. Download preview PDF.
References
- Born M., Oppenheimer R. (1927) Ann. d. Phys. 84, 457ADSMATHCrossRefGoogle Scholar
- Born M., Fock V. (1928) Zs. Phys. 51, 165ADSCrossRefGoogle Scholar
- Solov'ev E.A. (1989): Usp. Fiz. Nauk. 157, 437–476CrossRefGoogle Scholar
- Kvitsinsky Andrei A., Putterman Seth (1990): Exponentially suppressed transitions in an adiabatically driven system with a discrete spectrum. Phys. Rev. A42, 6303–6307ADSGoogle Scholar
- Suzko A.A. (1993): Phys. Part. Nucl. 24, 485 Multidimensional and three-body inverse scattering problems in the adiabatic representation”, Proc. Int.Conf. in Lecture Notes in Physics,” Quantum Inversion Theory and Applications, ed. H.V. von Geramb, 1993, Vol. 427, Springer-Verlag, Heidelberg, 67–106Google Scholar
- Suzko A.A. (1992): Exactly Solvable Tree-Body Models with Two-Center Potentials. Sov. J. Nucl. Phys. 55, 1359–1365; Supersymmetry, Geometric Nonadiabatic Phases in Diatomic Systems. Yad. Fiz. 56, 189–201MathSciNetGoogle Scholar
- Vinitsky S.I., Suzko A. A. (1990): Exactly Solvable Multidimensional and Tree-Particle Scattering Problems in the Adiabatic Representation. Sov. J. Nucl. Phys. 52, 442–451.Google Scholar
- Chadan K., Sabatier P.C. (1977,1989): Inverse Problems in Quantum Scattering Theory (Springer-Verlag, New York, Berlin/Heidelberg)MATHGoogle Scholar
- Zakhariev B.N., Suzko A.A. (1990): Potentials and Quantum Scattering: Direct and Inverse Problems (Springer-Verlag, New York, Berlin/Heidelberg)Google Scholar
- Hwang J.T., Pechukas Ph. (1977): The Adiabatic Theorem in the Complex Plane and the Semiclassical of Nonadiabatic Transition Amplidudes. J. Chem. Phys. 67, 4640–4653MathSciNetADSCrossRefGoogle Scholar
- Suzko A.A., Velicheva E.P. (1996): Exactly Soluble Two-Dimensional Models in the Adiabatic Representation. Physics of Atomic Nuclei 59, 1087–1103MathSciNetADSGoogle Scholar
- Suzko A.A., Velicheva E.P. (1996): Exactly Solvable Models and Investigation of Level Crossing. Phys. Part. Nucl. 27, 923Google Scholar
- Suzko A.A., Velicheva E.P. (1996): Proc. Intern. Conf. on Quantum Systems: New Trends and Methods. (Minsk, 4–7, June)Google Scholar
Copyright information
© Springer-Verlag Berlin Heidelberg 1997