No data available.
Please log in to see this content.
You have no subscription access to this content.
No metrics data to plot.
The attempt to load metrics for this article has failed.
The attempt to plot a graph for these metrics has failed.
Variational Bounds for the Potential in Terms of the S‐Wave Phase Shift
1.F. Calogero and A. Degasperis, J. Math. Phys. 9, 90 (1968); hereafter referred to as 1.
2.R. E. Bellman, Proc. Natl. Acad. Sci. U.S. 41, 743 (1955);
2.R. E. Kalaba, J. Math. Mech. 8, 519 (1959);
2.F. Calogero, J. Math. Phys. 4, 427 (1963);
2.R. E. Bellman and R. E. Kalaba, Quasilinearization and Nonlinear Boundary‐Value Problems (Elsevier Publ. Co., New York, 1965).
3.F. Calogero, Nuovo Cimento 27, 261 (1963);
3.F. Calogero, 27, 947 (1963); , Nuovo Cimento
3.F. Calogero, 28, 320 (1963); , Nuovo Cimento
3.Variable Phase Approach to Potential Scattering (Academic Press Inc., New York, 1967), Chaps. 9 and 14 and Appendix II.
4.Such variational expressions, originally introduced by L. Hulthén and J. Schwinger, are now discussed in most textbooks on scattering theory.
4.See, for instance, T. Y. Wu and T. Ohmura, Quantum Theory of Scattering (Prentice‐Hall, Inc., Englewood Cliffs, N.J., 1962);
4.M. L. Goldberger and K. M. Watson, Collision Theory (John Wiley & Sons, Inc., New York, 1964);
4.R. G. Newton, Scattering Theory of Waves and Particles, (McGraw‐Hill Book Co., New York, 1965).
5.T. Ohmura, Progr. Theoret. Phys. (Kyoto) 16, 231 (1956).
6.This formula follows trivially from Eqs. (2.22)–(2.24) of I.
7.The bound‐state normalization coefficient is defined by , where is the radial wavefunction of the bound state with energy normalized by the condition at the origin
8.A. K. Bose, Phys. Letters 7, 245 (1963).
9.For all special functions we adopt the notation of Higher Transcendental Functions, A. Erdélyi, Ed. (McGraw‐Hill Book Co., New York, 1953).
10.V. Bargmann, Proc. Natl. Acad. Sci. U.S. 38, 961 (1952).
11.In fact, it is easily seen that the left‐hand side of Eq. (3.6) is real even if z and λ are imaginary, since by the Kummer transformation it may be written in the form .
Article metrics loading...
Full text loading...