Singular factorizations, self-adjoint extensions, and applications to quantum many-body physics

Details Singular factorizations, self-adjoint extensions, and applications to quantum many-body physics Singular factorizations, self-adjoint extensions, and applications to quantum many-body physics

2005-10-12

arxiv.org/abs/math-ph/0510046v1

Physics

Mathematical Physics

17 pages, LaTex

Scientific paper

10.1088/0305-4470/39/5/004

We study self-adjoint operators defined by factorizing second order differential operators in first order ones. We discuss examples where such factorizations introduce singular interactions into simple quantum mechanical models like the harmonic oscillator or the free particle on the circle. The generalization of these examples to the many-body case yields quantum models of distinguishable and interacting particles in one dimensions which can be solved explicitly and by simple means. Our considerations lead us to a simple method to construct exactly solvable quantum many-body systems of Calogero-Sutherland type.

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