Abstract
For a system of N bosons in one space dimension with two-body δ-interactions the Hamiltonian can be defined in terms of the usual closed semi-bounded quadratic form. We approximate this Hamiltonian in norm resolvent sense by Schrödinger operators with rescaled two-body potentials, and we estimate the rate of this convergence.
Highlights
Short-range interactions with large scattering length in quantum mechanical systems of bosons or distinguishable particles are conveniently described by δ-potentials, unless the space dimension is three and the number of particles exceeds two [1, 2, 6]
This has a long tradition in physics and rigorous formulation in mathematics [1, 11, 12]
A mathematical justification of such idealized models based on manyparticle Schrodinger operators with suitably rescaled two-body potentials is still at the beginning [3, 14, 20]
Summary
Short-range interactions with large scattering length in quantum mechanical systems of bosons or distinguishable particles are conveniently described by δ-potentials, unless the space dimension is three and the number of particles exceeds two [1, 2, 6]. This has a long tradition in physics and rigorous formulation in mathematics [1, 11, 12]. A mathematical justification of such idealized models based on manyparticle Schrodinger operators with suitably rescaled two-body potentials is still at the beginning [3, 14, 20]. The Hilbert space of the system to be considered is the N-fold symmetric tensor product
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