144
3 Berggren Basis and Completeness Relations
References
1. G. Birkhoff, G.C. Rota, Am. Math. Mon. 67, 835 (1960)
2. E.C. Titchmarsh, Eigenfunction Expansions Associated with Second-order Differential Equations (Oxford University, Clarendon, 1958)
3. G. Fubini, Ann. Mat. Pura Appl. 20, 217 (1913)
4. L. Lichtenstein, Über eine Integro-Differentialgleichung und die Entwicklung willkürlicher
Funktionen nach deren Eigenfunktionen (Springer, Berlin, 1914)
5. H. Weyl, Math. Ann. 68, 220 (1910)
6. N. Dunford, J.T. Schwartz, Linear Operators (Wiley Classics Library, New York, 1988)
7. T. Berggren, Nucl. Phys. A 109, 265 (1968)
8. A. Messiah, Quantum Mechanics, vol. 1 and 2 (North Holland Publishing Co., Amsterdam,
1961)
9. R. Newton, Scattering Theory of Waves and Particles, 2nd edn. (Dover Publications, New York,
2013)
10. N. Michel, J. Math. Phys. 49, 022109 (2008)
11. P.M. Morse, H. Feshbach, Methods of Theoretical Physics (Mc Graw-Hill, New York, 1953)
12. R. Newton, J. Math. Phys. 1, 319 (1960)
13. N. Mukunda, Am. J. Phys. 49, 910 (1978)
14. M.J. Seaton, Rep. Prog. Phys. 46, 167 (1983)
15. Y.B. Zel’dovich, JETP (Sov. Phys.) 39, 776 (1960)
16. N. Hokkyo, Prog. Theor. Phys. 33, 1116 (1965)
17. W.J. Romo, Nucl. Phys. A 116, 617 (1968)
18. B. Gyarmati, T. Vertse, Nucl. Phys. A 160, 523 (1971)
19. G. Garcia-Calderon, R. Peierls, Nucl. Phys. A 265, 443 (1976)
20. N. Michel, W. Nazarewicz, M. Płoszajczak, J. Okołowicz, Phys. Rev. C 67, 054311 (2003)
21. V.I. Kukulin, V.M. Krasnopol’sky, J. Horᢠcek, Theory of Resonances (Kluwer Academic
Publishers, Dordrecht, 1989)
22. T. Vertse, P. Curutchet, R.J. Liotta, Lecture Notes in Physics, vol. 325 (Springer, Berlin, 1987),
p. 179
23. P. Lind, Phys. Rev. C 47, 1903 (1993)
24. B.F. Samsonov, J. Phys. A: Math. Gen. 38, L571 (2005)
25. T. Kato, Perturbation Theory for Linear Operators (Springer, Berlin, 1995)
26. M.R. Zirnbauer, J.J.M. Verbaarschot, H.A. Weidenmüller, Nucl. Phys. A 411, 161 (1983)
27. W.D. Heiss, W.H. Steeb, J. Math. Phys. 32, 3003 (1991)
28. W.D. Heiss, A.L. Sannino, Phys. Rev. A 43, 4159 (1991)
29. W. Heiss, J. Phys. A: Math. Gen. 37, 2455 (2004)
30. J. Okołowicz, M. Płoszajczak, I. Rotter, Phys. Rep. 374, 271 (2003)
31. M.V. Nikolaiev, V.S. Olkhovsky, Lett. Nuo. Cime. 8, 703 (1973)
32. J. Bang, F.A. Gareev, M.H. Gizzatkulov, S.A. Gonchanov, Nucl. Phys. A 309, 381 (1978)
33. W. Romo, Nucl. Phys. A 398, 525 (1983)
34. P. Lind, Phys. Rev. C 47, 1903 (1993)
35. P. Ring, P. Schuck, The Nuclear Many-Body Problem, 3rd ed. (Springer, Berlin, 2004)
36. D. Vautherin, M. Veneroni, Phys. Lett. B 25, 175 (1967)
37. P. Fraser, K. Amos, S. Karataglidis, L. Canton, G. Pisent, J.P. Svenne, Eur. Phys. J. A 35, 69
(2008)
38. E.I. Fredholm, Acta Math. 27, 365 (1903)
39. R.J. Liotta, E. Maglione, N. Sandulescu, T. Vertse, Phys. Lett. B 367, 1 (1996)
40. T. Vertse, R.J. Liotta, W. Nazarewicz, N. Sandulescu, A.T. Kruppa, Phys. Rev. C 57, 3089
(1998)
41. P. Lind, R.J. Liotta, E. Maglione, T. Vertse, Z. Phys. A 347, 231 (1994)
42. S. Saito, Suppl. Prog. Theor. Phys. 62, 11 (1977)
43. T. Myo, A. Ohnishi, K. Kat¯ o, Prog. Theor. Phys. 99, 801 (1998)
3 Berggren Basis and Completeness Relations
References
1. G. Birkhoff, G.C. Rota, Am. Math. Mon. 67, 835 (1960)
2. E.C. Titchmarsh, Eigenfunction Expansions Associated with Second-order Differential Equations (Oxford University, Clarendon, 1958)
3. G. Fubini, Ann. Mat. Pura Appl. 20, 217 (1913)
4. L. Lichtenstein, Über eine Integro-Differentialgleichung und die Entwicklung willkürlicher
Funktionen nach deren Eigenfunktionen (Springer, Berlin, 1914)
5. H. Weyl, Math. Ann. 68, 220 (1910)
6. N. Dunford, J.T. Schwartz, Linear Operators (Wiley Classics Library, New York, 1988)
7. T. Berggren, Nucl. Phys. A 109, 265 (1968)
8. A. Messiah, Quantum Mechanics, vol. 1 and 2 (North Holland Publishing Co., Amsterdam,
1961)
9. R. Newton, Scattering Theory of Waves and Particles, 2nd edn. (Dover Publications, New York,
2013)
10. N. Michel, J. Math. Phys. 49, 022109 (2008)
11. P.M. Morse, H. Feshbach, Methods of Theoretical Physics (Mc Graw-Hill, New York, 1953)
12. R. Newton, J. Math. Phys. 1, 319 (1960)
13. N. Mukunda, Am. J. Phys. 49, 910 (1978)
14. M.J. Seaton, Rep. Prog. Phys. 46, 167 (1983)
15. Y.B. Zel’dovich, JETP (Sov. Phys.) 39, 776 (1960)
16. N. Hokkyo, Prog. Theor. Phys. 33, 1116 (1965)
17. W.J. Romo, Nucl. Phys. A 116, 617 (1968)
18. B. Gyarmati, T. Vertse, Nucl. Phys. A 160, 523 (1971)
19. G. Garcia-Calderon, R. Peierls, Nucl. Phys. A 265, 443 (1976)
20. N. Michel, W. Nazarewicz, M. Płoszajczak, J. Okołowicz, Phys. Rev. C 67, 054311 (2003)
21. V.I. Kukulin, V.M. Krasnopol’sky, J. Horᢠcek, Theory of Resonances (Kluwer Academic
Publishers, Dordrecht, 1989)
22. T. Vertse, P. Curutchet, R.J. Liotta, Lecture Notes in Physics, vol. 325 (Springer, Berlin, 1987),
p. 179
23. P. Lind, Phys. Rev. C 47, 1903 (1993)
24. B.F. Samsonov, J. Phys. A: Math. Gen. 38, L571 (2005)
25. T. Kato, Perturbation Theory for Linear Operators (Springer, Berlin, 1995)
26. M.R. Zirnbauer, J.J.M. Verbaarschot, H.A. Weidenmüller, Nucl. Phys. A 411, 161 (1983)
27. W.D. Heiss, W.H. Steeb, J. Math. Phys. 32, 3003 (1991)
28. W.D. Heiss, A.L. Sannino, Phys. Rev. A 43, 4159 (1991)
29. W. Heiss, J. Phys. A: Math. Gen. 37, 2455 (2004)
30. J. Okołowicz, M. Płoszajczak, I. Rotter, Phys. Rep. 374, 271 (2003)
31. M.V. Nikolaiev, V.S. Olkhovsky, Lett. Nuo. Cime. 8, 703 (1973)
32. J. Bang, F.A. Gareev, M.H. Gizzatkulov, S.A. Gonchanov, Nucl. Phys. A 309, 381 (1978)
33. W. Romo, Nucl. Phys. A 398, 525 (1983)
34. P. Lind, Phys. Rev. C 47, 1903 (1993)
35. P. Ring, P. Schuck, The Nuclear Many-Body Problem, 3rd ed. (Springer, Berlin, 2004)
36. D. Vautherin, M. Veneroni, Phys. Lett. B 25, 175 (1967)
37. P. Fraser, K. Amos, S. Karataglidis, L. Canton, G. Pisent, J.P. Svenne, Eur. Phys. J. A 35, 69
(2008)
38. E.I. Fredholm, Acta Math. 27, 365 (1903)
39. R.J. Liotta, E. Maglione, N. Sandulescu, T. Vertse, Phys. Lett. B 367, 1 (1996)
40. T. Vertse, R.J. Liotta, W. Nazarewicz, N. Sandulescu, A.T. Kruppa, Phys. Rev. C 57, 3089
(1998)
41. P. Lind, R.J. Liotta, E. Maglione, T. Vertse, Z. Phys. A 347, 231 (1994)
42. S. Saito, Suppl. Prog. Theor. Phys. 62, 11 (1977)
43. T. Myo, A. Ohnishi, K. Kat¯ o, Prog. Theor. Phys. 99, 801 (1998)