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## We are the Theory group of LPS!

If you are interested in doing an internship with us, or want to visit and discuss, please contact any of our members.

We are a very collaborative group which covers a wide range of topics from material sciences (functional materials, topological and relativistic matter, magnetism and superconductivity...) and quantum systems (in low dimensions, under magnetic fields, in and out-of equilibrium...) to soft and bio- matter (colloids, liquid crystals...).

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## Recent Publications

G. Abramovici, “Incompatible Coulomb hamiltonian extensions”, vol. 10, no. 1, p. 7280, 2020. WebsiteAbstract
We revisit the resolution of the one-dimensional Schrödinger hamiltonian with a Coulomb λ/|x| potential. We examine among its self-adjoint extensions those which are compatible with physical conservation laws. In the one-dimensional semi-infinite case, we show that they are classified on a U(1) circle in the attractive case and on $${\boldsymbol{(}}{\mathbb{R}},{\boldsymbol{+}}{\boldsymbol{\infty }}{\boldsymbol{)}}$$(R,+∞) in the repulsive one. In the one-dimensional infinite case, we find a specific and original classification by studying the continuity of eigenfunctions. In all cases, different extensions are incompatible one with the other. For an actual experiment with an attractive potential, the bound spectrum can be used to discriminate which extension is the correct one.
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