Calculation of the scattering amplitude from discrete eigenvalues

Physical Review Letters

Volumn 91, Issue 13, 2003, Pages

  Matsuoka, H ^a   Grobe, R ^a  

^a ILLINOIS STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; EIGENVALUES AND EIGENFUNCTIONS; ELECTROMAGNETIC WAVE SCATTERING; SPECTRUM ANALYSIS;

SCATTERING AMPLITUDE;

QUANTUM THEORY;

EID: 0242384619     PISSN: 00319007     EISSN: 10797114     Source Type: Journal    
DOI: 10.1103/PhysRevLett.91.130405     Document Type: Article

References (11)

1. See, for example, standard textbooks such as L.I. Schiff, Quantum Mechanics (McGraw-Hill, New York, 1968);
2. R.G. Newton, Scattering Theory of Waves and Particles (Springer-Verlag, Heidelberg, 1982), 2nd ed.
3. J.D. Joannopoulos, R.D. Meade, and J.N. Winn, Photonic Crystals (Princeton University Press, Princeton, NJ, 1995).
4. The discrete wave number eigenvalues can be also used to construct a perturbation series for the phase shifts through the Fredholm theory of integral equations, where the infinite system limit, (Formula presented), is taken. See, for example, K. Gottfried, Quantum Mechanics (The Benjamin/Cummings Publishing Co., Reading, MA, 1966), Vol.�1.
5. J.H. Eberly, Am. J. Phys. 33, 771 (1965).
6. S. Menon, Q. Su, and R. Grobe, Phys. Rev. EPLEEE8 65, 051917 (2002).10.1103/PhysRevE.65.051917
7. F. Haake, Quantum Signatures of Classical Chaos (Springer-Verlag, Heidelberg, 1991).
8. H. Matsuoka and R. Grobe (to be published).
9. U. Fano and A.R. Rau, Atomic Collisions and Spectra (Academic, New York, 1986);
10. F.H.M. Faisal, Theory of Multiphoton Processes (Plenum Press, New York, 1987).
11. The statistics of the transmission intensity for a chaotic cavity has been studied within the random (Formula presented)-matrix theory in H.U. Baranger and P.A. Mello, Phys. Rev. Lett. 73, 142 (1994).10.1103/PhysRevLett.73.142