A solvable model for excitonic complexes in one dimension

Journal of Mathematical Physics

Volumn 38, Issue 8, 1997, Pages 4013-4022

  Markvardsen, Anders J ^a   Johnson, Neil F ^a  

^a UNIVERSITY OF OXFORD   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031481523     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.532082     Document Type: Article

References (16)

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2. K. Kheng, R. T. Cox, Y. M. Daubigne, F. Bassani, K. Saminadayar, and S. Tatarenko, Phys. Rev. Lett. 71, 1752 (1993). See also G. Finkelstein, H. Shtrikman, and I. Barjoseph, Phys. Rev. Lett. 74, 976 (1995) and A. J. Shields, M. Pepper, M. Y. Simmons, and D. A. Ritchie, Phys. Rev. B 52, 7841 (1995).
3. K. Kheng, R. T. Cox, Y. M. Daubigne, F. Bassani, K. Saminadayar, and S. Tatarenko, Phys. Rev. Lett. 71, 1752 (1993). See also G. Finkelstein, H. Shtrikman, and I. Barjoseph, Phys. Rev. Lett. 74, 976 (1995) and A. J. Shields, M. Pepper, M. Y. Simmons, and D. A. Ritchie, Phys. Rev. B 52, 7841 (1995).
4. W. Wegscheider, L. N. Pfeiffer, M. M. Dignam, A. Pinczuk, K. W. West, S. L. McCall, and R. Hull, Phys. Rev. Lett. 71, 4071 (1993).
5. L. D. Hallam, J. Weiss, and P. A. Maksym, Phys. Rev. B 53, 1452 (1996).
6. F. Calogero, J. Math. Phys. 10, 2191 (1969).
7. N. F. Johnson, J. Phys.: Condens. Matt. 7, 965 (1995).
8. M. Moshinsky, J. Phys. A: Math. Gen. 27, 4719 (1994).
9. P. Kurasov, J. Phys. A: Math. Gen. 29, 1767 (1996) and references therein.
10. K. Heun, Math. Ann. 33, 161 (1889).
11. F. M. Arscott, in Heun's Differential Equation, edited by A. Ronvenaux (Oxford, U.P., Oxford, 1995).
12. See the bibliography in Ref. 9.
13. H. E. Heine, Handbuch der kugelfunktionen (Reimer, Berlin, 1878).
14. Software for PC compatible computers running Window 3.1 is available from Dr. S. Slavyanov. It gives a graphical representation of Heun's differential equations, together with some additional tools for handling them. See the last page of S. Slavyanov, W. Lay, and A. Seeger in Ref. 9.
15. For the special case f = -g, the formula in Eq. (12) reduces to the trigonometric identity found by Calogero (Ref. 4).
16. 4 Parameter Δ is given in Eq. (4).