Physics – Mathematical Physics
Scientific paper
2006-09-19
J. Phys. A: Math. Theor. 40 (2007) 249-261
Physics
Mathematical Physics
15 pages, some misprints corrected, one example added, some references modified or added
Scientific paper
10.1088/1751-8113/40/2/004
We consider a system realized with one spinless quantum particle and an array of $N$ spins 1/2 in dimension one and three. We characterize all the Hamiltonians obtained as point perturbations of an assigned free dynamics in terms of some ``generalized boundary conditions''. For every boundary condition we give the explicit formula for the resolvent of the corresponding Hamiltonian. We discuss the problem of locality and give two examples of spin dependent point potentials that could be of interest as multi-component solvable models.
Cacciapuoti Claudio
Carlone Raffaele
Figari Rodolfo
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