Self-adjoint, globally defined Hamiltonian operators for systems with boundaries - Mathematical PhysicsReport as inadecuate




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Abstract: For a general self-adjoint Hamiltonian operator $H 0$ on the Hilbert space$L^2\RE^d$, we determine the set of all self-adjoint Hamiltonians $H$ on$L^2\RE^d$ that dynamically confine the system to an open set $\Omega \subset\RE^d$ while reproducing the action of $ H 0$ on an appropriate operatordomain. In the case $H 0=-\Delta +V$ we construct these Hamiltonians explicitlyshowing that they can be written in the form $H=H 0+ B$, where $B$ is asingular boundary potential and $H$ is self-adjoint on its maximal domain. Anapplication to the deformation quantization of one-dimensional systems withboundaries is also presented.



Author: Nuno Costa Dias, Andrea Posilicano, Joao Nuno Prata

Source: https://arxiv.org/



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