Scattering of quantized solitary waves in the cubic Schrödinger equation
The quantum mechanics for N particles interacting via a delta-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 Schrodinger 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 N-body bound state is derived in this approximation. The nonlinear Schrodinger 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.
- Research Organization:
- Laboratory for Nuclear Science and Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
- Sponsoring Organization:
- USDOE
- NSA Number:
- NSA-33-032015
- OSTI ID:
- 4009197
- Journal Information:
- Physical Review. D, Particles Fields, Vol. 13, Issue 2; Other Information: Orig. Receipt Date: 30-JUN-76; ISSN 0556-2821
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
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