Spin dependent point potentials in one and three dimensions

Details Spin dependent point potentials in one and three dimensions Spin dependent point potentials in one and three dimensions

2006-09-19

arxiv.org/abs/math-ph/0609055v2

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.

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