Inverse Scattering Problem for the Schrödinger’s Equation
ABSTRACT
The analytic properties of the scattering amplitude are discussed. And, the representation of the potential by the scattering amplitude is obtained.
Cite this paper
A. Durmagambetov and L. Fazilova, "Inverse Scattering Problem for the Schrödinger’s Equation," International Journal of Modern Nonlinear Theory and Application, Vol. 2 No. 4, 2013, pp. 244-246. doi: 10.4236/ijmnta.2013.24035.
A. Durmagambetov and L. Fazilova, "Inverse Scattering Problem for the Schrödinger’s Equation," International Journal of Modern Nonlinear Theory and Application, Vol. 2 No. 4, 2013, pp. 244-246. doi: 10.4236/ijmnta.2013.24035.
References
[1] L. D Faddeev, “Inverse Problem of Quantum Scattering Theory II,” Itogi Nauk Takh. Sov Probl Mat, Vol. 3, 1974, p. 93-180. [2] R. G. Newton, “New Result on the Inverse Scattering Problem in Three Dimensions,” Physical Review Letters, Vol. 43, No. 8, 1979, pp. 541-542. [3] R. G. Newton, “Inverse Scattering Three Dimensions,” Journal of Mathematical Physics, Vol. 21, No. 7, 1980, pp. 1698-1715. http://dx.doi.org/10.1063/1.524637 [4] E. Somersalo, et al., “Inverse Scattering Problem for the Schrodinger’s Equation in Three Dimensions: Connections between Exact and Approximate Methods,” 1988. [5] A. Y. Povzner, “On the Expansion of Arbitrary Functions in Characteristic Functions of the Operator ,” Matematicheskii Sbornik, Vol. 32, No. 74, 1953, pp. 109-156. [6] M. Birman, “On the Spectrum of Singular Boundary-Value Problems,” (Russian) Matematicheskii Sbornik, Vol. 55, No. 97, 1961, pp. 125-174. [7] H. Poincare, “Lecons de Mecanique Celeste,” 1910.
[1] L. D Faddeev, “Inverse Problem of Quantum Scattering Theory II,” Itogi Nauk Takh. Sov Probl Mat, Vol. 3, 1974, p. 93-180. [2] R. G. Newton, “New Result on the Inverse Scattering Problem in Three Dimensions,” Physical Review Letters, Vol. 43, No. 8, 1979, pp. 541-542. [3] R. G. Newton, “Inverse Scattering Three Dimensions,” Journal of Mathematical Physics, Vol. 21, No. 7, 1980, pp. 1698-1715. http://dx.doi.org/10.1063/1.524637 [4] E. Somersalo, et al., “Inverse Scattering Problem for the Schrodinger’s Equation in Three Dimensions: Connections between Exact and Approximate Methods,” 1988. [5] A. Y. Povzner, “On the Expansion of Arbitrary Functions in Characteristic Functions of the Operator ,” Matematicheskii Sbornik, Vol. 32, No. 74, 1953, pp. 109-156. [6] M. Birman, “On the Spectrum of Singular Boundary-Value Problems,” (Russian) Matematicheskii Sbornik, Vol. 55, No. 97, 1961, pp. 125-174. [7] H. Poincare, “Lecons de Mecanique Celeste,” 1910.