an:03994158
Zbl 0614.35086
Gutkin, Eug??ne
Quantum nonlinear Schr??dinger equation. I: Intertwining operators
EN
Ann. Inst. Henri Poincar??, Anal. Non Lin??aire 3, 285-314 (1986).
00151801
1986
j
35Q99 35G20 81T08
delta Bose gas; Bethe ansatz; commutation relations; second quantization; quantum nonlinear Schr??dinger equation; field theory; intertwining operators; Hamiltonian; Fock space
The quantum nonlinear Schr??dinger equation is studied as a model of the quantum (nonrelativistic) field theory in \(1+1\) dimensions. In {\S} 1 the calculus of intertwining operators \(P_ N\), \(P^*_ N\), \(P_ N^{*- 1}\), \(P_ N^{-1}\) on \({\mathcal H}_ N\) is developed which produce the equivalence of the N-particle Hamiltonian \(H_ N\) and the free Hamiltonian \(-\Delta_ N\). In {\S} 2 the intertwining operators on the Fock space are studied, which are the direct sums of the corresponding operators on \({\mathcal H}_ N\). This calculus is supposed to be the basis for subsequent publications on the explicit solution of an initial value problem for the nonlinear Schr??dinger equation.
J.Weidmann