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Scattering of quantized solitary waves in the cubic Schrödinger equation
Phys. Rev. D 13, 528 – Published 15 January, 1976
DOI: https://doi.org/10.1103/PhysRevD.13.528
Abstract
The quantum mechanics for particles interacting via a -function potential in one space dimension and one time dimension is known. The second-quantized description of this system has for its Euler-Lagrange equations of motion the cubic Schrödinger equation. This nonlinear differential equation supports solitary wave solutions. A quantization of these solitons reproduces the weak-coupling limit to the known quantum mechanics. The phase shift for two-body scattering and the energy of the -body bound state is derived in this approximation. The nonlinear Schrödinger equation is contrasted with the sine-Gordon theory in respect to the ideas which the classical solutions play in the description of the quantum states.
Comments & Replies
Comment on the semiclassical -soliton matrix
Original Article
Semiclassical scattering of quantized nonlinear waves
References (12)
- R. Jackiw and G. Woo, Phys. Rev. D 12, 1643 (1975)
- [9] [8] [3] [1]
- D. J. Kaup, J. Math. Phys. 16, 2036 (1975)
- H. Bethe, Z. Phys. 71, 205 (1931)
- C. N. Yang, Phys. Rev. 168, 1920 (1968)
- J. B. McGuire, J. Math. Phys. 5, 622 (1964)
- V. E. Zakharov and A. B. Shabat, Zh. Eksp. Teor. Fiz. 61, 118 (1971) [Sov. Phys.—JETP 34, 62 (1972)]
- L. D. Faddeev, Princeton report (unpublished)
- C. Nohl, Princeton report (unpublished)
Omitted endnote
Omitted endnote
- Sidney Coleman, Phys. Rev. D 11, 2088 (1975)