Universal elementary constituents of potential transformations shifting waves (qualitative theory)

Author

Chabanov, V. M.

Sofianos, S. A.

Zakhariev, B. N.

reference

[Sov. J. Part. & Nucl. 21 (1990) 384]

[Sov. J. Part. & Nucl. 23 (1992) 603]

[Sov. J. Part. & Nucl. 25 (1994) 662]

10 J. Neumann, E. Wigner, Phys. Z. 30 (1929) 465

11 A. A. Stahlhofen, Phys. Rev. A51 (1995) 934

12 F. H. Stillinger, D. R. Herrik, Phys. Rev. A 11 (1975) 446;

13 M. S. P. Eastham, H. Kalf, Schrödinger-Type Operators with continuous Spectr a. Pitman, London, 1982

14 F. Calogero, A. Degasperis, Lett. Nuovo Cim. 23 (1978) 143

15 F. Capasso, C. Sirtori, J. Faist, D. L. Sivco, S. N. G. Chu, A. Y. Cho, Nature 358 (1992) 565

16 B. N. Zakhariev, V. M. Chabanov, Fiz. Elem. Chastits At. Yadra 25 (1994) 1561

17 B. N. Zakhariev, Fiz. Elem. Chastits At. Yadra 23 (1992) 1387

18 B. N. Zakhariev, N. A. Kostov, E. B. Plekhanov, Fiz. Elem. Chastits At. Yadra 21 (1990) 914

19 B. N. Zakhariev, Lessons on Quantum Intuition, Dubna, JINR, 1996; in:

1 R. G. Newton, Scattering Theory of Waves and Particles, 2nd ed. Springer, New York, 1982

20 T. Stroh, B. N. Zakhariev Physica Scripta 55 (1997) 9

2 B. N. Zakhariev, A. A. Suzko, Direct and Inverse Problems, Springer, Heidelberg, 1990

3 K. Chadan, P. C. Sabatier, Inverse Problems in Quantum Scattering Theory, 2nd ed. Springer, Heidelberg, 1989

4 F. Cooper, A. Khare, U. Sukhatme, Phys. Rep. 251, No. 5 & 6 (1995) 268 (and Refs therein)

5 A. A. Andrianov, M. v. Ioffe, V. P. Spiridonov, Phys. Lett. A 174 (1993) 273;

6 D. Baye, J. Phys. A28 (1995) 5079 and references therein.

7 C. v. Sukumar, J. Phys. A 18 (1985) 2917, 2937;

8 J. Pöschel, E. Trubowitz, Inverse Spectral Theor y. Academic, New York. 1987

9 S. A. Sofianos, A. Papastylianos, H. Fiedeldey, K. Amos, L. J. Allen (to be published 1997)

J. Papademos, U. Sukhatme, A. Pagnamenta, Phys. Rev. A 48 (1992) 3525

J. Phys. A 21 (1988) L455

JINR Rapid Commun. 6 [45]

N. Meyer-Vernet, Am. J. Phys. 50 (1982) 353;

Proc. Conf. Inverse Problems: Proceedings of the International Conference, Montpellier, 1986 (Aca d. Press, New York) 141; 1990,

V. P. Berezovoy, A. I. Pashnev, Z. Phys. C 51 (1991) 525

size

0136 - 0143

keyword(s)

<KWD>Spectral weights variation

Bound and scattering states

Quantum intuition

Wave bunching

abstract

It is shown that the potential perturbation that shifts a chosen standing wave in space is a block of potential barrier and well for every wave bump between neighbouring knots. The algorithms shifting the range of the primary localization of a chosen bound state in a potential well of finite width are as well applicable to the scattering functions if states of the continuous spectrum are considered as bound states normalized to unity but distributed on an infinite interval with vanishing density. The potential perturbations of the same type on the half-axis concentrate the scattering wave at the origin, thus creating a bound state embedded into the continuous spectrum (zero width resonance).

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research article