Abstract
We will discuss a new type of an isoperimetric problem concerning a Hamiltonian with N point interactions in ℝd, d = 2, 3, all with the same coupling constant, placed at vertices of an equilateral polygon P N. We show that the ground state energy is locally maximized by a regular polygon and conjecture that the maximum is global; on the way we encounter an interesting geometric inequality. We will also mention some extensions of this problem.
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Exner, P. (2006). Point Interaction Polygons: An Isoperimetric Problem. In: Asch, J., Joye, A. (eds) Mathematical Physics of Quantum Mechanics. Lecture Notes in Physics, vol 690. Springer, Berlin, Heidelberg . https://doi.org/10.1007/3-540-34273-7_7
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DOI: https://doi.org/10.1007/3-540-34273-7_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-31026-6
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