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arXiv · 1912.03670

Self-Adjoint Extensions of Bipartite Hamiltonians

Daniel Lenz·Timon Weinmann·Melchior Wirth
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Abstract

We compute the deficiency spaces of operators of the form $H_A{\hat{\otimes}} I + I{\hat{\otimes}} H_B$, for symmetric $H_A$ and self-adjoint $H_B$. This enables us to construct self-adjoint extensions (if they exist) by means of von Neumann's theory. The structure of the deficiency spaces for this case was asserted already by Ibort, Marmo and Pérez-Pardo, but only proven under the restriction of $H_B$ having discrete, non-degenerate spectrum.

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Daniel Lenz, Timon Weinmann, Melchior Wirth. 2020-11-18. Self-Adjoint Extensions of Bipartite Hamiltonians. https://arxiv.org/abs/1912.03670

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