Dressing of Zero-Range Potentials into Realistic Molecular Potentials of Finite Range

• Autorzy: Leble S. , Ponomarev D.
• Języki publikacji: EN

Abstrakty

EN

The zero-range potentials of the radial Schrodinger equation and their dressing are investigated. A sequence of Darboux transformations involving a set of parameters yields solvable potentials of a finite-range with physically meaningful properties. In particular, the newly obtained potential is matched to that resulting from the ab initio computation methods in terms of discrete and continuous spectrum parameters. The approach, being a companion to conventional quantum simulation methods, combines symbolical and numerical calculations and is expected to work best for molecules with high spherical symmetry, typically fullerenes.

Słowa kluczowe

EN

effective potentials; zero-range potentials; Darboux transformation; dressingmethod

• Wydawca: Politechnika Gdańska
• Czasopismo: TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk
• Rocznik: 2010
• Tom: Vol. 14, No 1-2
• Strony: 29--34
• Opis fizyczny: Bibliogr. 18 poz., rys.

Twórcy

autor

Leble S.

autor

Ponomarev D.

• 1Gdansk University of Technology, Theoretical Physics and Quantum Informatics Department, Narutowicza 11/12, 80-223 Gdansk, Poland,

Bibliografia

• [1] Fermi E 1934 Il Nuovo Cimento 11 157
• [2] Breit G 1947 Phys. Rev. 71 215
• [3] Baz’ A I, Zel’dovich Ya B and Perelomov A M 1971 Scattering, Reactions, and Decays in Nonrelativistic Mechanics, Nauka, Moscow, Russia (in Russian)
• [4] Albeverio S, Gesztesy F, Hoegh-Krohn R and Holden H 1988 Solvable Models in Quantum Mechanics, Springer, New York
• [5] Demkov Yu N and Ostrovskii V N 1988 Zero-range Potentials and Their Applications in Atomic Physics, Plenum Press, New York
• [6] Drukarev G 1979 Adv. Quantum Chem. 11 251
• [7] Huang K 1963 Statistical Mechanics, Wiley, New York
• [8] Huang K and Yang C N 1957 Phys. Rev. 105 767
• [9] Derevianko A 2005 Phys. Rev. A 72 44701
• [10] Leble S B and Yalunin S 2005 Phys. Lett. A 339 83
• [11] Doktorov E V and Leble S B 2006 A Dressing Method in Mathematical Physics, Springer, London
• [12] Idziaszek Z and Callarco T 2006 Phys. Rev. Lett. 96 13201
• [13] Darboux G 1882 C. R. Acad. Sci Paris 94 1456
• [14] Crum M M 1955 Quart. J. Math. Oxford Ser. 6 (2) 121
• [15] Matveev V B and Salle M A 1991 Darboux Transformations and Solitons, Springer-Verlag, Berlin, Heidelberg
• [16] Messiah A 1961 Quantum Mechanics, North-Holland Publishing Company, The Netherlands
• [17] Madjet M E, Chakraborty H S and Manson S T 2007 Phys. Rev. Lett. 99 243003
• [18] Abramowitz M and Stegun I 1964 Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, Dover, New York