Differential operator related to the generalized superradiance integral equation

Journal of Mathematical Analysis and Applications

Volumn 369, Issue 1, 2010, Pages 101-111

  SenGupta, Indranil ^a  

^a TEXAS A AND M UNIVERSITY   (United States)

Author keywords

Bessel functions; Eigenvalue and eigenfunction; Gegenbauer polynomials; Quantum mechanics; Spherical and hyperspherical harmonics

Indexed keywords

EID: 77952583485     PISSN: 0022247X     EISSN: 10960813     Source Type: Journal    
DOI: 10.1016/j.jmaa.2010.02.034     Document Type: Article

References (16)

1. Slepian D., Pollak H.O. Prolate spheroidal wave functions, Fourier analysis and uncertainty, I. Bell Syst. Tech. J. 1961, 40:43-64.
2. Landau H.J., Pollak H.O. Prolate spheroidal wave functions, Fourier analysis and uncertainty, II. Bell Syst. Tech. J. 1961, 41:65-84.
3. Landau H.J., Pollak H.O. Prolate spheroidal wave functions, Fourier analysis and uncertainty, III. Bell Syst. Tech. J. 1962, 41:1295-1336.
4. Slepian D. Prolate spheroidal wave functions, Fourier analysis and uncertainty, IV: Extensions to many dimensions; Generalized prolate spheroidal functions. Bell Syst. Tech. J. 1964, 43:3009-3058.
5. Slepian D. Prolate spheroidal wave functions, Fourier analysis and uncertainty, V. Bell Syst. Tech. J. 1978, 57:1371-1430.
6. Grünbaum F.A., Longh L., Perlstadt M. Differential operators commuting with finite convolution integral operators: some non-abelian examples. SIAM J. Appl. Math. 1982, 42:941-955.
7. Dicke R.H. Coherence in spontaneous radiation process. Phys. Rev. 1954, 93(1):99-110.
8. Scully M.O., Fry E.S., Ooi C.H.R., Wódkiewicz K. Directed spontaneous emission from an extended ensemble of N atoms: timing is everything. Phys. Rev. Lett. 2006, 96:010501.
9. Scully M.O. Correlated spontaneous emission on the Volga. Laser Physics 2007, 17:635-846.
10. Svidzinsky A., Chang J.-T. Cooperative spontaneous emission as a many-body eigenvalue problem. Phys. Rev. A 2008, 77:043833-1-043833-4.
11. Scully M.O., Svidzinsky A. The effects of the N atom collective Lamb shift on single photon superradiance. Phys. Lett. A 2009, 373:1283-1286.
12. Watson G.N. A Treatise on the Theory of Bessel Functions 1980, Cambridge University Press.
13. Erdélyi A. Higher Transcendental Functions, vols. I and II 1953, McGraw-Hill.
14. Vilenkin N.Ja. Special Functions and the Theory of Group Representations 1968, American Mathematical Society.
15. A. Svidzinsky, J.-T. Chang, M.O. Scully, Cooperative spontaneous emission of N atoms: many-body eigenstates, their decay and analogy with radiation of N classical oscillators, preprint.
16. A. Svidzinsky, J.-T. Chang, E.A. Sete, M.O. Scully, Cooperative spontaneous emission of N atoms: many-body eigenstates, effect of virtual Lamb shift processes and analogy with radiation of N classical oscillators, preprint.